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Título : Combinatorics of Coxeter Groups Tipo de documento: documento electrónico Autores: Anders Bjorner ; SpringerLink (Online service) ; Francesco Brenti Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2005 Colección: Graduate Texts in Mathematics, ISSN 0072-5285 num. 231 Número de páginas: XIV, 366 p Il.: online resource ISBN/ISSN/DL: 978-3-540-27596-1 Idioma : Inglés (eng) Palabras clave: Mathematics Group theory Topological groups Lie Combinatorics Groups, Groups Theory and Generalizations Clasificación: 51 Matemáticas Resumen: Coxeter groups are of central importance in several areas of algebra, geometry, and combinatorics. This clear and rigorous exposition focuses on the combinatorial aspects of Coxeter groups, such as reduced expressions, partial order of group elements, enumeration, associated graphs and combinatorial cell complexes, and connections with combinatorial representation theory. While Coxeter groups have already been exposited from algebraic and geometric perspectives, this text is the first one to focus mainly on the combinatorial aspects of Coxeter groups. The first part of the book provides a self-contained introduction to combinatorial Coxeter group theory. The emphasis here is on the combinatorics of reduced decompositions, Bruhat order, weak order, and some aspects of root systems. The second part deals with more advanced topics, such as Kazhdan-Lusztig polynomials and representations, enumeration, and combinatorial descriptions of the classical finite and affine Weyl groups. A wide variety of exercises, ranging from easy to quite difficult are also included. The book will serve graduate students as well as researchers. Anders Björner is Professor of Mathematics at the Royal Institute of Technology in Stockholm, Sweden. Francesco Brenti is Professor of Mathematics at the University of Rome Nota de contenido: I -- The basics -- Bruhat order -- Weak order and reduced words -- Roots, games, and automata -- II -- Kazhdan-Lusztig and R-polynomials -- Kazhdan-Lusztig representations -- Enumeration -- Combinatorial Descriptions En línea: http://dx.doi.org/10.1007/3-540-27596-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35283 Combinatorics of Coxeter Groups [documento electrónico] / Anders Bjorner ; SpringerLink (Online service) ; Francesco Brenti . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2005 . - XIV, 366 p : online resource. - (Graduate Texts in Mathematics, ISSN 0072-5285; 231) .
ISBN : 978-3-540-27596-1
Idioma : Inglés (eng)
Palabras clave: Mathematics Group theory Topological groups Lie Combinatorics Groups, Groups Theory and Generalizations Clasificación: 51 Matemáticas Resumen: Coxeter groups are of central importance in several areas of algebra, geometry, and combinatorics. This clear and rigorous exposition focuses on the combinatorial aspects of Coxeter groups, such as reduced expressions, partial order of group elements, enumeration, associated graphs and combinatorial cell complexes, and connections with combinatorial representation theory. While Coxeter groups have already been exposited from algebraic and geometric perspectives, this text is the first one to focus mainly on the combinatorial aspects of Coxeter groups. The first part of the book provides a self-contained introduction to combinatorial Coxeter group theory. The emphasis here is on the combinatorics of reduced decompositions, Bruhat order, weak order, and some aspects of root systems. The second part deals with more advanced topics, such as Kazhdan-Lusztig polynomials and representations, enumeration, and combinatorial descriptions of the classical finite and affine Weyl groups. A wide variety of exercises, ranging from easy to quite difficult are also included. The book will serve graduate students as well as researchers. Anders Björner is Professor of Mathematics at the Royal Institute of Technology in Stockholm, Sweden. Francesco Brenti is Professor of Mathematics at the University of Rome Nota de contenido: I -- The basics -- Bruhat order -- Weak order and reduced words -- Roots, games, and automata -- II -- Kazhdan-Lusztig and R-polynomials -- Kazhdan-Lusztig representations -- Enumeration -- Combinatorial Descriptions En línea: http://dx.doi.org/10.1007/3-540-27596-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35283 Ejemplares
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Título : Compact Lie Groups Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Sepanski, Mark R Editorial: New York, NY : Springer New York Fecha de publicación: 2007 Colección: Graduate Texts in Mathematics, ISSN 0072-5285 num. 235 Número de páginas: XIII, 201 p Il.: online resource ISBN/ISSN/DL: 978-0-387-49158-5 Idioma : Inglés (eng) Palabras clave: Mathematics Associative rings Rings (Algebra) Matrix theory Algebra Topological groups Lie Mathematical analysis Analysis (Mathematics) Differential geometry Groups, Groups Linear and Multilinear Algebras, Theory Algebras Geometry Clasificación: 51 Matemáticas Resumen: Blending algebra, analysis, and topology, the study of compact Lie groups is one of the most beautiful areas of mathematics and a key stepping stone to the theory of general Lie groups. Assuming no prior knowledge of Lie groups, this book covers the structure and representation theory of compact Lie groups. Included is the construction of the Spin groups, Schur Orthogonality, the Peter–Weyl Theorem, the Plancherel Theorem, the Maximal Torus Theorem, the Commutator Theorem, the Weyl Integration and Character Formulas, the Highest Weight Classification, and the Borel–Weil Theorem. The necessary Lie algebra theory is also developed in the text with a streamlined approach focusing on linear Lie groups. Key Features: • Provides an approach that minimizes advanced prerequisites • Self-contained and systematic exposition requiring no previous exposure to Lie theory • Advances quickly to the Peter–Weyl Theorem and its corresponding Fourier theory • Streamlined Lie algebra discussion reduces the differential geometry prerequisite and allows a more rapid transition to the classification and construction of representations • Exercises sprinkled throughout This beginning graduate-level text, aimed primarily at Lie Groups courses and related topics, assumes familiarity with elementary concepts from group theory, analysis, and manifold theory. Students, research mathematicians, and physicists interested in Lie theory will find this text very useful Nota de contenido: Compact Lie Groups -- Representations -- HarmoniC Analysis -- Lie Algebras -- Abelian Lie Subgroups and Structure -- Roots and Associated Structures -- Highest Weight Theory En línea: http://dx.doi.org/10.1007/978-0-387-49158-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34488 Compact Lie Groups [documento electrónico] / SpringerLink (Online service) ; Sepanski, Mark R . - New York, NY : Springer New York, 2007 . - XIII, 201 p : online resource. - (Graduate Texts in Mathematics, ISSN 0072-5285; 235) .
ISBN : 978-0-387-49158-5
Idioma : Inglés (eng)
Palabras clave: Mathematics Associative rings Rings (Algebra) Matrix theory Algebra Topological groups Lie Mathematical analysis Analysis (Mathematics) Differential geometry Groups, Groups Linear and Multilinear Algebras, Theory Algebras Geometry Clasificación: 51 Matemáticas Resumen: Blending algebra, analysis, and topology, the study of compact Lie groups is one of the most beautiful areas of mathematics and a key stepping stone to the theory of general Lie groups. Assuming no prior knowledge of Lie groups, this book covers the structure and representation theory of compact Lie groups. Included is the construction of the Spin groups, Schur Orthogonality, the Peter–Weyl Theorem, the Plancherel Theorem, the Maximal Torus Theorem, the Commutator Theorem, the Weyl Integration and Character Formulas, the Highest Weight Classification, and the Borel–Weil Theorem. The necessary Lie algebra theory is also developed in the text with a streamlined approach focusing on linear Lie groups. Key Features: • Provides an approach that minimizes advanced prerequisites • Self-contained and systematic exposition requiring no previous exposure to Lie theory • Advances quickly to the Peter–Weyl Theorem and its corresponding Fourier theory • Streamlined Lie algebra discussion reduces the differential geometry prerequisite and allows a more rapid transition to the classification and construction of representations • Exercises sprinkled throughout This beginning graduate-level text, aimed primarily at Lie Groups courses and related topics, assumes familiarity with elementary concepts from group theory, analysis, and manifold theory. Students, research mathematicians, and physicists interested in Lie theory will find this text very useful Nota de contenido: Compact Lie Groups -- Representations -- HarmoniC Analysis -- Lie Algebras -- Abelian Lie Subgroups and Structure -- Roots and Associated Structures -- Highest Weight Theory En línea: http://dx.doi.org/10.1007/978-0-387-49158-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34488 Ejemplares
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Título : Complex Kleinian Groups Tipo de documento: documento electrónico Autores: Angel Cano ; SpringerLink (Online service) ; Juan Pablo Navarrete ; Seade, José Editorial: Basel : Springer Basel Fecha de publicación: 2013 Otro editor: Imprint: Birkhäuser Colección: Progress in Mathematics, ISSN 0743-1643 num. 303 Número de páginas: XX, 272 p Il.: online resource ISBN/ISSN/DL: 978-3-0348-0481-3 Idioma : Inglés (eng) Palabras clave: Mathematics Topological groups Lie Dynamics Ergodic theory Functions of complex variables Dynamical Systems and Theory Groups, Groups Several Complex Variables Analytic Spaces Clasificación: 51 Matemáticas Resumen: This monograph lays down the foundations of the theory of complex Kleinian groups, a “newborn” area of mathematics whose origin can be traced back to the work of Riemann, Poincaré, Picard and many others. Kleinian groups are, classically, discrete groups of conformal automorphisms of the Riemann sphere, and these can themselves be regarded as groups of holomorphic automorphisms of the complex projective line CP1. When we go into higher dimensions, there is a dichotomy: Should we look at conformal automorphisms of the n-sphere? or should we look at holomorphic automorphisms of higher dimensional complex projective spaces? These two theories differ in higher dimensions. In the first case we are talking about groups of isometries of real hyperbolic spaces, an area of mathematics with a long-standing tradition; in the second, about an area of mathematics that is still in its infancy, and this is the focus of study in this monograph. It brings together several important areas of mathematics, e.g. classical Kleinian group actions, complex hyperbolic geometry, crystallographic groups and the uniformization problem for complex manifolds Nota de contenido: Preface -- Introduction -- Acknowledgments -- 1 A glance of the classical theory -- 2 Complex hyperbolic geometry -- 3 Complex Kleinian groups -- 4 Geometry and dynamics of automorphisms of P2C -- 5 Kleinian groups with a control group -- 6 The limit set in dimension two -- 7 On the dynamics of discrete subgroups of PU(n,1) -- 8 Projective orbifolds and dynamics in dimension two -- 9 Complex Schottky groups -- 10 Kleinian groups and twistor theory -- Bibliography -- Index. En línea: http://dx.doi.org/10.1007/978-3-0348-0481-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32420 Complex Kleinian Groups [documento electrónico] / Angel Cano ; SpringerLink (Online service) ; Juan Pablo Navarrete ; Seade, José . - Basel : Springer Basel : Imprint: Birkhäuser, 2013 . - XX, 272 p : online resource. - (Progress in Mathematics, ISSN 0743-1643; 303) .
ISBN : 978-3-0348-0481-3
Idioma : Inglés (eng)
Palabras clave: Mathematics Topological groups Lie Dynamics Ergodic theory Functions of complex variables Dynamical Systems and Theory Groups, Groups Several Complex Variables Analytic Spaces Clasificación: 51 Matemáticas Resumen: This monograph lays down the foundations of the theory of complex Kleinian groups, a “newborn” area of mathematics whose origin can be traced back to the work of Riemann, Poincaré, Picard and many others. Kleinian groups are, classically, discrete groups of conformal automorphisms of the Riemann sphere, and these can themselves be regarded as groups of holomorphic automorphisms of the complex projective line CP1. When we go into higher dimensions, there is a dichotomy: Should we look at conformal automorphisms of the n-sphere? or should we look at holomorphic automorphisms of higher dimensional complex projective spaces? These two theories differ in higher dimensions. In the first case we are talking about groups of isometries of real hyperbolic spaces, an area of mathematics with a long-standing tradition; in the second, about an area of mathematics that is still in its infancy, and this is the focus of study in this monograph. It brings together several important areas of mathematics, e.g. classical Kleinian group actions, complex hyperbolic geometry, crystallographic groups and the uniformization problem for complex manifolds Nota de contenido: Preface -- Introduction -- Acknowledgments -- 1 A glance of the classical theory -- 2 Complex hyperbolic geometry -- 3 Complex Kleinian groups -- 4 Geometry and dynamics of automorphisms of P2C -- 5 Kleinian groups with a control group -- 6 The limit set in dimension two -- 7 On the dynamics of discrete subgroups of PU(n,1) -- 8 Projective orbifolds and dynamics in dimension two -- 9 Complex Schottky groups -- 10 Kleinian groups and twistor theory -- Bibliography -- Index. En línea: http://dx.doi.org/10.1007/978-3-0348-0481-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32420 Ejemplares
Signatura Medio Ubicación Sub-localización Sección Estado ningún ejemplar Geometry and Dynamics of Groups and Spaces / SpringerLink (Online service) ; Mikhail Kapranov ; Yuri Ivanovich Manin ; Pieter Moree ; Sergiy Kolyada ; Leonid Potyagailo (2008)
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 : Infinite Groups: Geometric, Combinatorial and Dynamical Aspects Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Laurent Bartholdi ; Tullio Ceccherini-Silberstein ; Tatiana Smirnova-Nagnibeda ; Andrzej Zuk Editorial: Basel : Birkhäuser Basel Fecha de publicación: 2005 Colección: Progress in Mathematics num. 248 Número de páginas: VIII, 416 p Il.: online resource ISBN/ISSN/DL: 978-3-7643-7447-1 Idioma : Inglés (eng) Palabras clave: Mathematics Group theory Topological groups Lie Operator Differential geometry Algebraic topology Combinatorics Theory and Generalizations Groups, Groups Geometry Topology Clasificación: 51 Matemáticas Resumen: This book offers a panorama of recent advances in the theory of infinite groups. It contains survey papers contributed by leading specialists in group theory and other areas of mathematics. Topics addressed in the book include amenable groups, Kaehler groups, automorphism groups of rooted trees, rigidity, C*-algebras, random walks on groups, pro-p groups, Burnside groups, parafree groups, and Fuchsian groups. The accent is put on strong connections between group theory and other areas of mathematics, such as dynamical systems, geometry, operator algebras, probability theory, and others. This interdisciplinary approach makes the book interesting to a large mathematical audience. Contributors: G. Baumslag A.V. Borovik T. Delzant W. Dicks E. Formanek R. Grigorchuk M. Gromov P. de la Harpe A. Lubotzky W. Lück A.G. Myasnikov C. Pache G. Pisier A. Shalev S. Sidki E. Zelmanov Nota de contenido: Parafree Groups -- The Finitary Andrews-Curtis Conjecture -- Cuts in Kähler Groups -- Algebraic Mapping-Class Groups of Orientable Surfaces with Boundaries -- Solved and Unsolved Problems Around One Group -- Cubature Formulas, Geometrical Designs, Reproducing Kernels, and Markov Operators -- Survey on Classifying Spaces for Families of Subgroups -- Are Unitarizable Groups Amenable? -- Probabilistic Group Theory and Fuchsian Groups -- Just Non-(abelian by P-type) Groups -- Infinite Algebras and Pro-p Groups En línea: http://dx.doi.org/10.1007/3-7643-7447-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35349 Infinite Groups: Geometric, Combinatorial and Dynamical Aspects [documento electrónico] / SpringerLink (Online service) ; Laurent Bartholdi ; Tullio Ceccherini-Silberstein ; Tatiana Smirnova-Nagnibeda ; Andrzej Zuk . - Basel : Birkhäuser Basel, 2005 . - VIII, 416 p : online resource. - (Progress in Mathematics; 248) .
ISBN : 978-3-7643-7447-1
Idioma : Inglés (eng)
Palabras clave: Mathematics Group theory Topological groups Lie Operator Differential geometry Algebraic topology Combinatorics Theory and Generalizations Groups, Groups Geometry Topology Clasificación: 51 Matemáticas Resumen: This book offers a panorama of recent advances in the theory of infinite groups. It contains survey papers contributed by leading specialists in group theory and other areas of mathematics. Topics addressed in the book include amenable groups, Kaehler groups, automorphism groups of rooted trees, rigidity, C*-algebras, random walks on groups, pro-p groups, Burnside groups, parafree groups, and Fuchsian groups. The accent is put on strong connections between group theory and other areas of mathematics, such as dynamical systems, geometry, operator algebras, probability theory, and others. This interdisciplinary approach makes the book interesting to a large mathematical audience. Contributors: G. Baumslag A.V. Borovik T. Delzant W. Dicks E. Formanek R. Grigorchuk M. Gromov P. de la Harpe A. Lubotzky W. Lück A.G. Myasnikov C. Pache G. Pisier A. Shalev S. Sidki E. Zelmanov Nota de contenido: Parafree Groups -- The Finitary Andrews-Curtis Conjecture -- Cuts in Kähler Groups -- Algebraic Mapping-Class Groups of Orientable Surfaces with Boundaries -- Solved and Unsolved Problems Around One Group -- Cubature Formulas, Geometrical Designs, Reproducing Kernels, and Markov Operators -- Survey on Classifying Spaces for Families of Subgroups -- Are Unitarizable Groups Amenable? -- Probabilistic Group Theory and Fuchsian Groups -- Just Non-(abelian by P-type) Groups -- Infinite Algebras and Pro-p Groups En línea: http://dx.doi.org/10.1007/3-7643-7447-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35349 Ejemplares
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