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Título : Topological Methods in Group Theory Tipo de documento: documento electrónico Autores: Ross Geoghegan ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2008 Colección: Graduate Texts in Mathematics, ISSN 0072-5285 num. 243 Número de páginas: XVI, 473 p. 41 illus Il.: online resource ISBN/ISSN/DL: 978-0-387-74614-2 Idioma : Inglés (eng) Palabras clave: Mathematics Group theory Topological groups Lie Topology Groups, Groups Theory and Generalizations Clasificación: 51 Matemáticas Resumen: Topological Methods in Group Theory is about the interplay between algebraic topology and the theory of infinite discrete groups. The author has kept three kinds of readers in mind: graduate students who have had an introductory course in algebraic topology and who need a bridge from common knowledge to the current research literature in geometric, combinatorial and homological group theory; group theorists who would like to know more about the topological side of their subject but who have been too long away from topology; and manifold topologists, both high- and low-dimensional, since the book contains much basic material on proper homotopy and locally finite homology not easily found elsewhere. The book focuses on two main themes: 1. Topological Finiteness Properties of groups (generalizing the classical notions of "finitely generated" and "finitely presented"); 2. Asymptotic Aspects of Infinite Groups (generalizing the classical notion of "the number of ends of a group"). Illustrative examples treated in some detail include: Bass-Serre theory, Coxeter groups, Thompson groups, Whitehead's contractible 3-manifold, Davis's exotic contractible manifolds in dimensions greater than three, the Bestvina-Brady Theorem, and the Bieri-Neumann-Strebel invariant. The book also includes a highly geometrical treatment of Poincaré duality (via cells and dual cells) to bring out the topological meaning of Poincaré duality groups. To keep the length reasonable and the focus clear, it is assumed that the reader knows or can easily learn the necessary algebra (which is clearly summarized) but wants to see the topology done in detail. Apart from the introductory material, most of the mathematics presented here has not appeared in book form before Nota de contenido: Algebraic Topology for Group Theory -- CW Complexes and Homotopy -- Cellular Homology -- Fundamental Group and Tietze Transformation -- Some Techniques in Homotopy Theory -- Elementary Geometric Topology -- Finiteness Properties of Groups -- The Borel Construction and Bass-Serre Theory -- Topological Finiteness Properties and Dimension of Groups -- Homological Finiteness Properties of Groups -- Finiteness Properties of Some Important Groups -- Locally Finite Algebraic Topology for Group Theory -- Locally Finite CW Complexes and Proper Homotopy -- Locally Finite Homology -- Cohomology of CW Complexes -- Topics in the Cohomology of Infinite Groups -- Cohomology of Groups and Ends of Covering Spaces -- Filtered Ends of Pairs of Groups -- Poincaré Duality in Manifolds and Groups -- Homotopical Group Theory -- The Fundamental Group At Infinity -- Higher homotopy theory of groups -- Three Essays -- Three Essays En línea: http://dx.doi.org/10.1007/978-0-387-74614-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34194 Topological Methods in Group Theory [documento electrónico] / Ross Geoghegan ; SpringerLink (Online service) . - New York, NY : Springer New York, 2008 . - XVI, 473 p. 41 illus : online resource. - (Graduate Texts in Mathematics, ISSN 0072-5285; 243) .
ISBN : 978-0-387-74614-2
Idioma : Inglés (eng)
Palabras clave: Mathematics Group theory Topological groups Lie Topology Groups, Groups Theory and Generalizations Clasificación: 51 Matemáticas Resumen: Topological Methods in Group Theory is about the interplay between algebraic topology and the theory of infinite discrete groups. The author has kept three kinds of readers in mind: graduate students who have had an introductory course in algebraic topology and who need a bridge from common knowledge to the current research literature in geometric, combinatorial and homological group theory; group theorists who would like to know more about the topological side of their subject but who have been too long away from topology; and manifold topologists, both high- and low-dimensional, since the book contains much basic material on proper homotopy and locally finite homology not easily found elsewhere. The book focuses on two main themes: 1. Topological Finiteness Properties of groups (generalizing the classical notions of "finitely generated" and "finitely presented"); 2. Asymptotic Aspects of Infinite Groups (generalizing the classical notion of "the number of ends of a group"). Illustrative examples treated in some detail include: Bass-Serre theory, Coxeter groups, Thompson groups, Whitehead's contractible 3-manifold, Davis's exotic contractible manifolds in dimensions greater than three, the Bestvina-Brady Theorem, and the Bieri-Neumann-Strebel invariant. The book also includes a highly geometrical treatment of Poincaré duality (via cells and dual cells) to bring out the topological meaning of Poincaré duality groups. To keep the length reasonable and the focus clear, it is assumed that the reader knows or can easily learn the necessary algebra (which is clearly summarized) but wants to see the topology done in detail. Apart from the introductory material, most of the mathematics presented here has not appeared in book form before Nota de contenido: Algebraic Topology for Group Theory -- CW Complexes and Homotopy -- Cellular Homology -- Fundamental Group and Tietze Transformation -- Some Techniques in Homotopy Theory -- Elementary Geometric Topology -- Finiteness Properties of Groups -- The Borel Construction and Bass-Serre Theory -- Topological Finiteness Properties and Dimension of Groups -- Homological Finiteness Properties of Groups -- Finiteness Properties of Some Important Groups -- Locally Finite Algebraic Topology for Group Theory -- Locally Finite CW Complexes and Proper Homotopy -- Locally Finite Homology -- Cohomology of CW Complexes -- Topics in the Cohomology of Infinite Groups -- Cohomology of Groups and Ends of Covering Spaces -- Filtered Ends of Pairs of Groups -- Poincaré Duality in Manifolds and Groups -- Homotopical Group Theory -- The Fundamental Group At Infinity -- Higher homotopy theory of groups -- Three Essays -- Three Essays En línea: http://dx.doi.org/10.1007/978-0-387-74614-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34194 Ejemplares
Signatura Medio Ubicación Sub-localización Sección Estado ningún ejemplar Complex, Contact and Symmetric Manifolds / SpringerLink (Online service) ; Oldrich Kowalski ; Emilio Musso ; Domenico Perrone (2005)
Título : Complex, Contact and Symmetric Manifolds : In Honor of L. Vanhecke Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Oldrich Kowalski ; Emilio Musso ; Domenico Perrone Editorial: Boston, MA : Birkhäuser Boston Fecha de publicación: 2005 Colección: Progress in Mathematics num. 234 Número de páginas: X, 278 p Il.: online resource ISBN/ISSN/DL: 978-0-8176-4424-6 Idioma : Inglés (eng) Palabras clave: Mathematics Topological groups Lie Global analysis (Mathematics) Manifolds Geometry Differential geometry Algebraic topology Complex manifolds Analysis and on Groups, Groups Topology Cell Complexes (incl. Diff.Topology) Clasificación: 51 Matemáticas Resumen: This volume contains research and survey articles by well known and respected mathematicians on differential geometry and topology that have been collected and dedicated in honor of Lieven Vanhecke, as a tribute to his many fruitful and inspiring contributions to these fields. The papers, all written with the necessary introductory and contextual material, describe recent developments and research trends in spectral geometry, the theory of geodesics and curvature, contact and symplectic geometry, complex geometry, algebraic topology, homogeneous and symmetric spaces, and various applications of partial differential equations and differential systems to geometry. One of the key strengths of these articles is their appeal to non-specialists, as well as researchers and differential geometers. Contributors: D.E. Blair; E. Boeckx; A.A. Borisenko; G. Calvaruso; V. Cortés; P. de Bartolomeis; J.C. Díaz-Ramos; M. Djoric; C. Dunn; M. Fernández; A. Fujiki; E. García-Río; P.B. Gilkey; O. Gil-Medrano; L. Hervella; O. Kowalski; V. Muñoz; M. Pontecorvo; A.M. Naveira; T. Oguro; L. Schäfer; K. Sekigawa; C-L. Terng; K. Tsukada; Z. Vlášek; E. Wang; and J.A. Wolf Nota de contenido: Curvature of Contact Metric Manifolds -- A Case for Curvature: the Unit Tangent Bundle -- Convex Hypersurfaces in Hadamard Manifolds -- Contact Metric Geometry of the Unit Tangent Sphere Bundle -- Topological-antitopological Fusion Equations, Pluriharmonic Maps and Special Kähler Manifolds -- ?2 and ?-Deformation Theory for Holomorphic and Symplectic Manifolds -- Commutative Condition on the Second Fundamental Form of CR-submanifolds of Maximal CR-dimension of a Kähler Manifold -- The Geography of Non-Formal Manifolds -- Total Scalar Curvatures of Geodesic Spheres and of Boundaries of Geodesic Disks -- Curvature Homogeneous Pseudo-Riemannian Manifolds which are not Locally Homogeneous -- On Hermitian Geometry of Complex Surfaces -- Unit Vector Fields that are Critical Points of the Volume and of the Energy: Characterization and Examples -- On 3D-Riemannian Manifolds with Prescribed Ricci Eigenvalues -- Two Problems in Real and Complex Integral Geometry -- Notes on the Goldberg Conjecture in Dimension Four -- Curved Flats, Exterior Differential Systems, and Conservation Laws -- Symmetric Submanifolds of Riemannian Symmetric Spaces and Symmetric R-spaces -- Complex Forms of Quaternionic Symmetric Spaces En línea: http://dx.doi.org/10.1007/b138831 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35181 Complex, Contact and Symmetric Manifolds : In Honor of L. Vanhecke [documento electrónico] / SpringerLink (Online service) ; Oldrich Kowalski ; Emilio Musso ; Domenico Perrone . - Boston, MA : Birkhäuser Boston, 2005 . - X, 278 p : online resource. - (Progress in Mathematics; 234) .
ISBN : 978-0-8176-4424-6
Idioma : Inglés (eng)
Palabras clave: Mathematics Topological groups Lie Global analysis (Mathematics) Manifolds Geometry Differential geometry Algebraic topology Complex manifolds Analysis and on Groups, Groups Topology Cell Complexes (incl. Diff.Topology) Clasificación: 51 Matemáticas Resumen: This volume contains research and survey articles by well known and respected mathematicians on differential geometry and topology that have been collected and dedicated in honor of Lieven Vanhecke, as a tribute to his many fruitful and inspiring contributions to these fields. The papers, all written with the necessary introductory and contextual material, describe recent developments and research trends in spectral geometry, the theory of geodesics and curvature, contact and symplectic geometry, complex geometry, algebraic topology, homogeneous and symmetric spaces, and various applications of partial differential equations and differential systems to geometry. One of the key strengths of these articles is their appeal to non-specialists, as well as researchers and differential geometers. Contributors: D.E. Blair; E. Boeckx; A.A. Borisenko; G. Calvaruso; V. Cortés; P. de Bartolomeis; J.C. Díaz-Ramos; M. Djoric; C. Dunn; M. Fernández; A. Fujiki; E. García-Río; P.B. Gilkey; O. Gil-Medrano; L. Hervella; O. Kowalski; V. Muñoz; M. Pontecorvo; A.M. Naveira; T. Oguro; L. Schäfer; K. Sekigawa; C-L. Terng; K. Tsukada; Z. Vlášek; E. Wang; and J.A. Wolf Nota de contenido: Curvature of Contact Metric Manifolds -- A Case for Curvature: the Unit Tangent Bundle -- Convex Hypersurfaces in Hadamard Manifolds -- Contact Metric Geometry of the Unit Tangent Sphere Bundle -- Topological-antitopological Fusion Equations, Pluriharmonic Maps and Special Kähler Manifolds -- ?2 and ?-Deformation Theory for Holomorphic and Symplectic Manifolds -- Commutative Condition on the Second Fundamental Form of CR-submanifolds of Maximal CR-dimension of a Kähler Manifold -- The Geography of Non-Formal Manifolds -- Total Scalar Curvatures of Geodesic Spheres and of Boundaries of Geodesic Disks -- Curvature Homogeneous Pseudo-Riemannian Manifolds which are not Locally Homogeneous -- On Hermitian Geometry of Complex Surfaces -- Unit Vector Fields that are Critical Points of the Volume and of the Energy: Characterization and Examples -- On 3D-Riemannian Manifolds with Prescribed Ricci Eigenvalues -- Two Problems in Real and Complex Integral Geometry -- Notes on the Goldberg Conjecture in Dimension Four -- Curved Flats, Exterior Differential Systems, and Conservation Laws -- Symmetric Submanifolds of Riemannian Symmetric Spaces and Symmetric R-spaces -- Complex Forms of Quaternionic Symmetric Spaces En línea: http://dx.doi.org/10.1007/b138831 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35181 Ejemplares
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Título : Eisenstein Series and Applications Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Wee Teck Gan ; Stephen S. Kudla ; Yuri Tschinkel Editorial: Boston, MA : Birkhäuser Boston Fecha de publicación: 2008 Colección: Progress in Mathematics num. 258 Número de páginas: X, 314 p Il.: online resource ISBN/ISSN/DL: 978-0-8176-4639-4 Idioma : Inglés (eng) Palabras clave: Mathematics Algebraic geometry Topological groups Lie Applied mathematics Engineering Geometry Number theory Theory Applications of Groups, Groups Clasificación: 51 Matemáticas Resumen: Eisenstein series are an essential ingredient in the spectral theory of automorphic forms and an important tool in the theory of L-functions. They have also been exploited extensively by number theorists for many arithmetic purposes. Bringing together contributions from areas that are not usually interacting with each other, this volume introduces diverse users of Eisenstein series to a variety of important applications. With this juxtaposition of perspectives, the reader obtains deeper insights into the arithmetic of Eisenstein series. The exposition focuses on the common structural properties of Eisenstein series occurring in many related applications that have arisen in several recent developments in arithmetic: Arakelov intersection theory on Shimura varieties, special values of L-functions and Iwasawa theory, and equidistribution of rational/integer points on homogeneous varieties. Key questions that are considered include: Is it possible to identify a class of Eisenstein series whose Fourier coefficients (resp. special values) encode significant arithmetic information? Do such series fit into p-adic families? Are the Eisenstein series that arise in counting problems of this type? Contributors include: B. Brubaker, D. Bump, J. Franke, S. Friedberg, W.T. Gan, P. Garrett, M. Harris, D. Jiang, S.S. Kudla, E. Lapid, K. Prasanna, A. Raghuram, F. Shahidi, R. Takloo-Bighash Nota de contenido: Twisted Weyl Group Multiple Dirichlet Series: The Stable Case -- A Topological Model for Some Summand of the Eisenstein Cohomology of Congruence Subgroups -- The Saito-Kurokawa Space of PGSp4 and Its Transfer to Inner Forms -- Values of Archimedean Zeta Integrals for Unitary Groups -- A Simple Proof of Rationality of Siegel-Weil Eisenstein Series -- Residues of Eisenstein Series and Related Problems -- Some Extensions of the Siegel-Weil Formula -- A Remark on Eisenstein Series -- Arithmetic Aspects of the Theta Correspondence and Periods of Modular Forms -- Functoriality and Special Values of L-Functions -- Bounds for Matrix Coefficients and Arithmetic Applications En línea: http://dx.doi.org/10.1007/978-0-8176-4639-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34270 Eisenstein Series and Applications [documento electrónico] / SpringerLink (Online service) ; Wee Teck Gan ; Stephen S. Kudla ; Yuri Tschinkel . - Boston, MA : Birkhäuser Boston, 2008 . - X, 314 p : online resource. - (Progress in Mathematics; 258) .
ISBN : 978-0-8176-4639-4
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebraic geometry Topological groups Lie Applied mathematics Engineering Geometry Number theory Theory Applications of Groups, Groups Clasificación: 51 Matemáticas Resumen: Eisenstein series are an essential ingredient in the spectral theory of automorphic forms and an important tool in the theory of L-functions. They have also been exploited extensively by number theorists for many arithmetic purposes. Bringing together contributions from areas that are not usually interacting with each other, this volume introduces diverse users of Eisenstein series to a variety of important applications. With this juxtaposition of perspectives, the reader obtains deeper insights into the arithmetic of Eisenstein series. The exposition focuses on the common structural properties of Eisenstein series occurring in many related applications that have arisen in several recent developments in arithmetic: Arakelov intersection theory on Shimura varieties, special values of L-functions and Iwasawa theory, and equidistribution of rational/integer points on homogeneous varieties. Key questions that are considered include: Is it possible to identify a class of Eisenstein series whose Fourier coefficients (resp. special values) encode significant arithmetic information? Do such series fit into p-adic families? Are the Eisenstein series that arise in counting problems of this type? Contributors include: B. Brubaker, D. Bump, J. Franke, S. Friedberg, W.T. Gan, P. Garrett, M. Harris, D. Jiang, S.S. Kudla, E. Lapid, K. Prasanna, A. Raghuram, F. Shahidi, R. Takloo-Bighash Nota de contenido: Twisted Weyl Group Multiple Dirichlet Series: The Stable Case -- A Topological Model for Some Summand of the Eisenstein Cohomology of Congruence Subgroups -- The Saito-Kurokawa Space of PGSp4 and Its Transfer to Inner Forms -- Values of Archimedean Zeta Integrals for Unitary Groups -- A Simple Proof of Rationality of Siegel-Weil Eisenstein Series -- Residues of Eisenstein Series and Related Problems -- Some Extensions of the Siegel-Weil Formula -- A Remark on Eisenstein Series -- Arithmetic Aspects of the Theta Correspondence and Periods of Modular Forms -- Functoriality and Special Values of L-Functions -- Bounds for Matrix Coefficients and Arithmetic Applications En línea: http://dx.doi.org/10.1007/978-0-8176-4639-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34270 Ejemplares
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Título : Geometry and Dynamics of Groups and Spaces : In Memory of Alexander Reznikov Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Mikhail Kapranov ; Yuri Ivanovich Manin ; Pieter Moree ; Sergiy Kolyada ; Leonid Potyagailo Editorial: Basel : Birkhäuser Basel Fecha de publicación: 2008 Colección: Progress in Mathematics num. 265 Número de páginas: XXIX, 742 p Il.: online resource ISBN/ISSN/DL: 978-3-7643-8608-5 Idioma : Inglés (eng) Palabras clave: Mathematics Topological groups Lie Dynamics Ergodic theory Geometry Differential geometry Algebraic topology Groups, Groups Dynamical Systems and Theory Topology Clasificación: 51 Matemáticas Nota de contenido: Analytic Topology of Groups, Actions, Strings and Varieties -- Analytic Topology of Groups, Actions, Strings and Varieties -- Research Articles -- Jørgensen’s Inequality for Non-Archimedean Metric Spaces -- The Hypoelliptic Dirac Operator -- Generalized Operads and Their Inner Cohomomorphisms -- Chern Character for Twisted Complexes -- (C, F)-Actions in Ergodic Theory -- Homomorphic Images of Branch Groups, and Serre’s Property (FA) -- On Nori’s Fundamental Group Scheme -- The Reidemeister Number of Any Automorphism of a Baumslag-Solitar Group is Infinite -- Pentagon Relation for the Quantum Dilogarithm and Quantized M 0,5 cyc -- Geodesic Flow on the Normal Congruence of a Minimal Surface -- The Chern Character of a Parabolic Bundle, and a Parabolic Corollary of Reznikov’s Theorem -- Kleinian Groups in Higher Dimensions -- A ?-bimodules and Serre A ?-functors -- Geometrization of Probability -- Milnor Invariants and l-Class Groups -- Three Topological Properties of Small Eigenfunctions on Hyperbolic Surfaces -- Quantum p-adic Spaces and Quantum p-adic Groups -- Convolution Equations on Lattices: Periodic Solutions with Values in a Prime Characteristic Field En línea: http://dx.doi.org/10.1007/978-3-7643-8608-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34399 Geometry and Dynamics of Groups and Spaces : In Memory of Alexander Reznikov [documento electrónico] / SpringerLink (Online service) ; Mikhail Kapranov ; Yuri Ivanovich Manin ; Pieter Moree ; Sergiy Kolyada ; Leonid Potyagailo . - Basel : Birkhäuser Basel, 2008 . - XXIX, 742 p : online resource. - (Progress in Mathematics; 265) .
ISBN : 978-3-7643-8608-5
Idioma : Inglés (eng)
Palabras clave: Mathematics Topological groups Lie Dynamics Ergodic theory Geometry Differential geometry Algebraic topology Groups, Groups Dynamical Systems and Theory Topology Clasificación: 51 Matemáticas Nota de contenido: Analytic Topology of Groups, Actions, Strings and Varieties -- Analytic Topology of Groups, Actions, Strings and Varieties -- Research Articles -- Jørgensen’s Inequality for Non-Archimedean Metric Spaces -- The Hypoelliptic Dirac Operator -- Generalized Operads and Their Inner Cohomomorphisms -- Chern Character for Twisted Complexes -- (C, F)-Actions in Ergodic Theory -- Homomorphic Images of Branch Groups, and Serre’s Property (FA) -- On Nori’s Fundamental Group Scheme -- The Reidemeister Number of Any Automorphism of a Baumslag-Solitar Group is Infinite -- Pentagon Relation for the Quantum Dilogarithm and Quantized M 0,5 cyc -- Geodesic Flow on the Normal Congruence of a Minimal Surface -- The Chern Character of a Parabolic Bundle, and a Parabolic Corollary of Reznikov’s Theorem -- Kleinian Groups in Higher Dimensions -- A ?-bimodules and Serre A ?-functors -- Geometrization of Probability -- Milnor Invariants and l-Class Groups -- Three Topological Properties of Small Eigenfunctions on Hyperbolic Surfaces -- Quantum p-adic Spaces and Quantum p-adic Groups -- Convolution Equations on Lattices: Periodic Solutions with Values in a Prime Characteristic Field En línea: http://dx.doi.org/10.1007/978-3-7643-8608-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34399 Ejemplares
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Título : Introduction to Quantum Groups Tipo de documento: documento electrónico Autores: George Lusztig ; SpringerLink (Online service) Editorial: Boston : Birkhäuser Boston Fecha de publicación: 2010 Colección: Modern Birkhäuser Classics Número de páginas: XIV, 352 p Il.: online resource ISBN/ISSN/DL: 978-0-8176-4717-9 Idioma : Inglés (eng) Palabras clave: Mathematics Algebra Group theory Topological groups Lie Physics Quantum physics Theory and Generalizations Groups, Groups Mathematical Methods in Clasificación: 51 Matemáticas Resumen: The quantum groups discussed in this book are the quantized enveloping algebras introduced by Drinfeld and Jimbo in 1985, or variations thereof. It is shown that these algebras have natural integral forms that can be specialized at roots of 1 and yield new objects, which include quantum versions of the semi-simple groups over fields of positive characteristic. The theory of quantum groups has led to a new, extremely rigid structure, in which the objects of the theory are provided with canonical bases having rather remarkable properties. This book contains an extensive treatment of the theory of canonical bases in the framework of perverse sheaves. The theory developed in the book includes the case of quantum affine enveloping algebras and, more generally, the quantum analogs of the Kac–Moody Lie algebras. Introduction to Quantum Groups will be of interest to mathematicians working in the representation theory of Lie groups and Lie algebras, knot theorists, theoretical physicists, and graduate students. Since large parts of the book are independent of the theory of perverse sheaves, the work may also be used as a textbook. **************************************** There is no doubt that this volume is a very remarkable piece of work...Its appearance represents a landmark in the mathematical literature. —Bulletin of the London Mathematical Society This book is an important contribution to the field and can be recommended especially to mathematicians working in the field. —EMS Newsletter The present book gives a very efficient presentation of an important part of quantum group theory. It is a valuable contribution to the literature. —Mededelingen van het Wiskundig Lusztig's book is very well written and seems to be flawless...Obviously, this will be the standard reference book for the material presented and anyone interested in the Drinfeld–Jimbo algebras will have to study it very carefully. —ZAA [T]his book is much more than an 'introduction to quantum groups.' It contains a wealth of material. In addition to the many important results (of which several are new–at least in the generality presented here), there are plenty of useful calculations (commutator formulas, generalized quantum Serre relations, etc.). —Zentralblatt MATH Nota de contenido: THE DRINFELD JIMBO ALGERBRA U -- The Algebra f -- Weyl Group, Root Datum -- The Algebra U -- The Quasi--Matrix -- The Symmetries of an Integrable U-Module -- Complete Reducibility Theorems -- Higher Order Quantum Serre Relations -- GEOMETRIC REALIZATION OF F -- Review of the Theory of Perverse Sheaves -- Quivers and Perverse Sheaves -- Fourier-Deligne Transform -- Periodic Functors -- Quivers with Automorphisms -- The Algebras and k -- The Signed Basis of f -- KASHIWARAS OPERATIONS AND APPLICATIONS -- The Algebra -- Kashiwara’s Operators in Rank 1 -- Applications -- Study of the Operators -- Inner Product on -- Bases at ? -- Cartan Data of Finite Type -- Positivity of the Action of Fi, Ei in the Simply-Laced Case -- CANONICAL BASIS OF U -- The Algebra -- Canonical Bases in Certain Tensor Products -- The Canonical Basis -- Inner Product on -- Based Modules -- Bases for Coinvariants and Cyclic Permutations -- A Refinement of the Peter-Weyl Theorem -- The Canonical Topological Basis of -- CHANGE OF RINGS -- The Algebra -- Commutativity Isomorphism -- Relation with Kac-Moody Lie Algebras -- Gaussian Binomial Coefficients at Roots of 1 -- The Quantum Frobenius Homomorphism -- The Algebras -- BRAID GROUP ACTION -- The Symmetries of U -- Symmetries and Inner Product on f -- Braid Group Relations -- Symmetries and U+ -- Integrality Properties of the Symmetries -- The ADE Case En línea: http://dx.doi.org/10.1007/978-0-8176-4717-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33539 Introduction to Quantum Groups [documento electrónico] / George Lusztig ; SpringerLink (Online service) . - Boston : Birkhäuser Boston, 2010 . - XIV, 352 p : online resource. - (Modern Birkhäuser Classics) .
ISBN : 978-0-8176-4717-9
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebra Group theory Topological groups Lie Physics Quantum physics Theory and Generalizations Groups, Groups Mathematical Methods in Clasificación: 51 Matemáticas Resumen: The quantum groups discussed in this book are the quantized enveloping algebras introduced by Drinfeld and Jimbo in 1985, or variations thereof. It is shown that these algebras have natural integral forms that can be specialized at roots of 1 and yield new objects, which include quantum versions of the semi-simple groups over fields of positive characteristic. The theory of quantum groups has led to a new, extremely rigid structure, in which the objects of the theory are provided with canonical bases having rather remarkable properties. This book contains an extensive treatment of the theory of canonical bases in the framework of perverse sheaves. The theory developed in the book includes the case of quantum affine enveloping algebras and, more generally, the quantum analogs of the Kac–Moody Lie algebras. Introduction to Quantum Groups will be of interest to mathematicians working in the representation theory of Lie groups and Lie algebras, knot theorists, theoretical physicists, and graduate students. Since large parts of the book are independent of the theory of perverse sheaves, the work may also be used as a textbook. **************************************** There is no doubt that this volume is a very remarkable piece of work...Its appearance represents a landmark in the mathematical literature. —Bulletin of the London Mathematical Society This book is an important contribution to the field and can be recommended especially to mathematicians working in the field. —EMS Newsletter The present book gives a very efficient presentation of an important part of quantum group theory. It is a valuable contribution to the literature. —Mededelingen van het Wiskundig Lusztig's book is very well written and seems to be flawless...Obviously, this will be the standard reference book for the material presented and anyone interested in the Drinfeld–Jimbo algebras will have to study it very carefully. —ZAA [T]his book is much more than an 'introduction to quantum groups.' It contains a wealth of material. In addition to the many important results (of which several are new–at least in the generality presented here), there are plenty of useful calculations (commutator formulas, generalized quantum Serre relations, etc.). —Zentralblatt MATH Nota de contenido: THE DRINFELD JIMBO ALGERBRA U -- The Algebra f -- Weyl Group, Root Datum -- The Algebra U -- The Quasi--Matrix -- The Symmetries of an Integrable U-Module -- Complete Reducibility Theorems -- Higher Order Quantum Serre Relations -- GEOMETRIC REALIZATION OF F -- Review of the Theory of Perverse Sheaves -- Quivers and Perverse Sheaves -- Fourier-Deligne Transform -- Periodic Functors -- Quivers with Automorphisms -- The Algebras and k -- The Signed Basis of f -- KASHIWARAS OPERATIONS AND APPLICATIONS -- The Algebra -- Kashiwara’s Operators in Rank 1 -- Applications -- Study of the Operators -- Inner Product on -- Bases at ? -- Cartan Data of Finite Type -- Positivity of the Action of Fi, Ei in the Simply-Laced Case -- CANONICAL BASIS OF U -- The Algebra -- Canonical Bases in Certain Tensor Products -- The Canonical Basis -- Inner Product on -- Based Modules -- Bases for Coinvariants and Cyclic Permutations -- A Refinement of the Peter-Weyl Theorem -- The Canonical Topological Basis of -- CHANGE OF RINGS -- The Algebra -- Commutativity Isomorphism -- Relation with Kac-Moody Lie Algebras -- Gaussian Binomial Coefficients at Roots of 1 -- The Quantum Frobenius Homomorphism -- The Algebras -- BRAID GROUP ACTION -- The Symmetries of U -- Symmetries and Inner Product on f -- Braid Group Relations -- Symmetries and U+ -- Integrality Properties of the Symmetries -- The ADE Case En línea: http://dx.doi.org/10.1007/978-0-8176-4717-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33539 Ejemplares
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