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Título : Developments and Trends in Infinite-Dimensional Lie Theory Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Neeb, Karl-Hermann ; Pianzola, Arturo Editorial: Boston : Birkhäuser Boston Fecha de publicación: 2011 Colección: Progress in Mathematics num. 288 Número de páginas: VIII, 492 p. 9 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-4741-4 Idioma : Inglés (eng) Palabras clave: Mathematics Algebra Algebraic geometry Group theory Topological groups Lie Geometry Groups, Groups Theory and Generalizations Clasificación: 51 Matemáticas Resumen: This collection of invited expository articles focuses on recent developments and trends in infinite-dimensional Lie theory, which has become one of the core areas of modern mathematics. The book is divided into three parts: infinite-dimensional Lie (super-)algebras, geometry of infinite-dimensional Lie (transformation) groups, and representation theory of infinite-dimensional Lie groups. Part (A) is mainly concerned with the structure and representation theory of infinite-dimensional Lie algebras and contains articles on the structure of direct-limit Lie algebras, extended affine Lie algebras and loop algebras, as well as representations of loop algebras and Kac–Moody superalgebras. The articles in Part (B) examine connections between infinite-dimensional Lie theory and geometry. The topics range from infinite-dimensional groups acting on fiber bundles, corresponding characteristic classes and gerbes, to Jordan-theoretic geometries and new results on direct-limit groups. The analytic representation theory of infinite-dimensional Lie groups is still very much underdeveloped. The articles in Part (C) develop new, promising methods based on heat kernels, multiplicity freeness, Banach–Lie–Poisson spaces, and infinite-dimensional generalizations of reductive Lie groups. Contributors: B. Allison, D. Beltita, W. Bertram, J. Faulkner, Ph. Gille, H. Glöckner, K.-H. Neeb, E. Neher, I. Penkov, A. Pianzola, D. Pickrell, T.S. Ratiu, N.R. Scheithauer, C. Schweigert, V. Serganova, K. Styrkas, K. Waldorf, and J.A. Wolf Nota de contenido: Preface -- Part A: Infinite-Dimensional Lie (Super-)Algebras -- Isotopy for Extended Affine Lie Algebras and Lie Tori -- Remarks on the Isotriviality of Multiloop Algebras -- Extended Affine Lie Algebras and Other Generalizations of Affine Lie Algebras – A Survey -- Tensor Representations of Classical Locally Finite Lie Algebras -- Lie Algebras, Vertex Algebras, and Automorphic Forms -- Kac–Moody Superalgebras and Integrability -- Part B: Geometry of Infinite-Dimensional Lie (Transformation) Groups -- Jordan Structures and Non-Associative Geometry -- Direct Limits of Infinite-Dimensional Lie Groups -- Lie Groups of Bundle Automorphisms and Their Extensions -- Gerbes and Lie Groups -- Part C: Representation Theory of Infinite-Dimensional Lie Groups Functional Analytic Background for a Theory of Infinite- Dimensional Reductive Lie Groups -- Heat Kernel Measures and Critical Limits -- Coadjoint Orbits and the Beginnings of a Geometric Representation Theory -- Infinite-Dimensional Multiplicity-Free Spaces I: Limits of Compact Commutative Spaces -- Index En línea: http://dx.doi.org/10.1007/978-0-8176-4741-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33092 Developments and Trends in Infinite-Dimensional Lie Theory [documento electrónico] / SpringerLink (Online service) ; Neeb, Karl-Hermann ; Pianzola, Arturo . - Boston : Birkhäuser Boston, 2011 . - VIII, 492 p. 9 illus : online resource. - (Progress in Mathematics; 288) .
ISBN : 978-0-8176-4741-4
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebra Algebraic geometry Group theory Topological groups Lie Geometry Groups, Groups Theory and Generalizations Clasificación: 51 Matemáticas Resumen: This collection of invited expository articles focuses on recent developments and trends in infinite-dimensional Lie theory, which has become one of the core areas of modern mathematics. The book is divided into three parts: infinite-dimensional Lie (super-)algebras, geometry of infinite-dimensional Lie (transformation) groups, and representation theory of infinite-dimensional Lie groups. Part (A) is mainly concerned with the structure and representation theory of infinite-dimensional Lie algebras and contains articles on the structure of direct-limit Lie algebras, extended affine Lie algebras and loop algebras, as well as representations of loop algebras and Kac–Moody superalgebras. The articles in Part (B) examine connections between infinite-dimensional Lie theory and geometry. The topics range from infinite-dimensional groups acting on fiber bundles, corresponding characteristic classes and gerbes, to Jordan-theoretic geometries and new results on direct-limit groups. The analytic representation theory of infinite-dimensional Lie groups is still very much underdeveloped. The articles in Part (C) develop new, promising methods based on heat kernels, multiplicity freeness, Banach–Lie–Poisson spaces, and infinite-dimensional generalizations of reductive Lie groups. Contributors: B. Allison, D. Beltita, W. Bertram, J. Faulkner, Ph. Gille, H. Glöckner, K.-H. Neeb, E. Neher, I. Penkov, A. Pianzola, D. Pickrell, T.S. Ratiu, N.R. Scheithauer, C. Schweigert, V. Serganova, K. Styrkas, K. Waldorf, and J.A. Wolf Nota de contenido: Preface -- Part A: Infinite-Dimensional Lie (Super-)Algebras -- Isotopy for Extended Affine Lie Algebras and Lie Tori -- Remarks on the Isotriviality of Multiloop Algebras -- Extended Affine Lie Algebras and Other Generalizations of Affine Lie Algebras – A Survey -- Tensor Representations of Classical Locally Finite Lie Algebras -- Lie Algebras, Vertex Algebras, and Automorphic Forms -- Kac–Moody Superalgebras and Integrability -- Part B: Geometry of Infinite-Dimensional Lie (Transformation) Groups -- Jordan Structures and Non-Associative Geometry -- Direct Limits of Infinite-Dimensional Lie Groups -- Lie Groups of Bundle Automorphisms and Their Extensions -- Gerbes and Lie Groups -- Part C: Representation Theory of Infinite-Dimensional Lie Groups Functional Analytic Background for a Theory of Infinite- Dimensional Reductive Lie Groups -- Heat Kernel Measures and Critical Limits -- Coadjoint Orbits and the Beginnings of a Geometric Representation Theory -- Infinite-Dimensional Multiplicity-Free Spaces I: Limits of Compact Commutative Spaces -- Index En línea: http://dx.doi.org/10.1007/978-0-8176-4741-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33092 Ejemplares
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Título : Harmonic Analysis on Symmetric Spaces—Euclidean Space, the Sphere, and the Poincaré Upper Half-Plane Tipo de documento: documento electrónico Autores: Terras, Audrey ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2013 Otro editor: Imprint: Springer Número de páginas: XVII, 413 p. 83 illus., 32 illus. in color Il.: online resource ISBN/ISSN/DL: 978-1-4614-7972-7 Idioma : Inglés (eng) Palabras clave: Mathematics Group theory Topological groups Lie Harmonic analysis Fourier Functions of complex variables Special functions Abstract Analysis Theory and Generalizations Groups, Groups a Complex Variable Clasificación: 51 Matemáticas Resumen: This unique text is an introduction to harmonic analysis on the simplest symmetric spaces, namely Euclidean space, the sphere, and the Poincaré upper half plane. This book is intended for beginning graduate students in mathematics or researchers in physics or engineering. Written with an informal style, the book places an emphasis on motivation, concrete examples, history, and, above all, applications in mathematics, statistics, physics, and engineering. Many corrections, new topics, and updates have been incorporated in this new edition. These include discussions of the work of P. Sarnak and others making progress on various conjectures on modular forms, the work of T. Sunada, Marie-France Vignéras, Carolyn Gordon, and others on Mark Kac's question "Can you hear the shape of a drum?", Ramanujan graphs, wavelets, quasicrystals, modular knots, triangle and quaternion groups, computations of Maass waveforms, and, finally, the author's comparisons of continuous theory with the finite analogues. Topics featured throughout the text include inversion formulas for Fourier transforms, central limit theorems, Poisson's summation formula and applications in crystallography and number theory, applications of spherical harmonic analysis to the hydrogen atom, the Radon transform, non-Euclidean geometry on the Poincaré upper half plane H or unit disc and applications to microwave engineering, fundamental domains in H for discrete groups G, tessellations of H from such discrete group actions, automorphic forms, the Selberg trace formula and its applications in spectral theory as well as number theory Nota de contenido: Chapter 1 Flat Space. Fourier Analysis on R^m. -- 1.1 Distributions or Generalized Functions -- 1.2 Fourier Integrals -- 1.3 Fourier Series and the Poisson Summation Formula -- 1.4 Mellin Transforms, Epstein and Dedekind Zeta Functions -- 1.5 Finite Symmetric Spaces, Wavelets, Quasicrystals, Weyl’s Criterion for Uniform Distribution -- Chapter 2 A Compact Symmetric Space--The Sphere -- 2.1 Fourier Analysis on the Sphere -- 2.2 O(3) and R^3. The Radon Transform -- Chapter 3 The Poincaré Upper Half-Plane -- 3.1 Hyperbolic Geometry -- 3.2 Harmonic Analysis on H -- 3.3 Fundamental Domains for Discrete Subgroups G of G = SL(2, R) -- 3.4 Modular of Automorphic Forms--Classical -- 3.5 Automorphic Forms--Not So Classical--Maass Waveforms -- 3.6 Modular Forms and Dirichlet Series. Hecke Theory and Generalizations -- References -- Index En línea: http://dx.doi.org/10.1007/978-1-4614-7972-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32374 Harmonic Analysis on Symmetric Spaces—Euclidean Space, the Sphere, and the Poincaré Upper Half-Plane [documento electrónico] / Terras, Audrey ; SpringerLink (Online service) . - New York, NY : Springer New York : Imprint: Springer, 2013 . - XVII, 413 p. 83 illus., 32 illus. in color : online resource.
ISBN : 978-1-4614-7972-7
Idioma : Inglés (eng)
Palabras clave: Mathematics Group theory Topological groups Lie Harmonic analysis Fourier Functions of complex variables Special functions Abstract Analysis Theory and Generalizations Groups, Groups a Complex Variable Clasificación: 51 Matemáticas Resumen: This unique text is an introduction to harmonic analysis on the simplest symmetric spaces, namely Euclidean space, the sphere, and the Poincaré upper half plane. This book is intended for beginning graduate students in mathematics or researchers in physics or engineering. Written with an informal style, the book places an emphasis on motivation, concrete examples, history, and, above all, applications in mathematics, statistics, physics, and engineering. Many corrections, new topics, and updates have been incorporated in this new edition. These include discussions of the work of P. Sarnak and others making progress on various conjectures on modular forms, the work of T. Sunada, Marie-France Vignéras, Carolyn Gordon, and others on Mark Kac's question "Can you hear the shape of a drum?", Ramanujan graphs, wavelets, quasicrystals, modular knots, triangle and quaternion groups, computations of Maass waveforms, and, finally, the author's comparisons of continuous theory with the finite analogues. Topics featured throughout the text include inversion formulas for Fourier transforms, central limit theorems, Poisson's summation formula and applications in crystallography and number theory, applications of spherical harmonic analysis to the hydrogen atom, the Radon transform, non-Euclidean geometry on the Poincaré upper half plane H or unit disc and applications to microwave engineering, fundamental domains in H for discrete groups G, tessellations of H from such discrete group actions, automorphic forms, the Selberg trace formula and its applications in spectral theory as well as number theory Nota de contenido: Chapter 1 Flat Space. Fourier Analysis on R^m. -- 1.1 Distributions or Generalized Functions -- 1.2 Fourier Integrals -- 1.3 Fourier Series and the Poisson Summation Formula -- 1.4 Mellin Transforms, Epstein and Dedekind Zeta Functions -- 1.5 Finite Symmetric Spaces, Wavelets, Quasicrystals, Weyl’s Criterion for Uniform Distribution -- Chapter 2 A Compact Symmetric Space--The Sphere -- 2.1 Fourier Analysis on the Sphere -- 2.2 O(3) and R^3. The Radon Transform -- Chapter 3 The Poincaré Upper Half-Plane -- 3.1 Hyperbolic Geometry -- 3.2 Harmonic Analysis on H -- 3.3 Fundamental Domains for Discrete Subgroups G of G = SL(2, R) -- 3.4 Modular of Automorphic Forms--Classical -- 3.5 Automorphic Forms--Not So Classical--Maass Waveforms -- 3.6 Modular Forms and Dirichlet Series. Hecke Theory and Generalizations -- References -- Index En línea: http://dx.doi.org/10.1007/978-1-4614-7972-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32374 Ejemplares
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Título : The Unity of Mathematics : In Honor of the Ninetieth Birthday of I.M. Gelfand Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Etingof, Pavel ; Retakh, Vladimir ; Singer, I. M Editorial: Boston, MA : Birkhäuser Boston Fecha de publicación: 2006 Colección: Progress in Mathematics num. 244 Número de páginas: XXII, 632 p. 41 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-4467-3 Idioma : Inglés (eng) Palabras clave: Mathematics Algebraic geometry Group theory K-theory Topological groups Lie Geometry Physics Mathematical Methods in Groups, Groups K-Theory Theory and Generalizations Clasificación: 51 Matemáticas Resumen: A tribute to the vision and legacy of Israel Moiseevich Gelfand, the invited papers in this volume reflect the unity of mathematics as a whole, with particular emphasis on the many connections among the fields of geometry, physics, and representation theory. Written by leading mathematicians, the text is broadly divided into two sections: the first is devoted to developments at the intersection of geometry and physics, and the second to representation theory and algebraic geometry. Topics include conformal field theory, K-theory, noncommutative geometry, gauge theory, representations of infinite-dimensional Lie algebras, and various aspects of the Langlands program. Graduate students and researchers will benefit from and find inspiration in this broad and unique work, which brings together fundamental results in a number of disciplines and highlights the rewards of an interdisciplinary approach to mathematics and physics. Contributors: M. Atiyah; A. Braverman; H. Brezis; T. Coates; A. Connes; S. Debacker; V. Drinfeld; L.D. Faddeev; M. Finkelberg; D. Gaitsgory; I.M. Gelfand; A. Givental; D. Kazhdan; M. Kontsevich; B. Kostant; C-H. Liu; K. Liu; G. Lusztig; D. McDuff; M. Movshev; N.A. Nekrasov; A. Okounkov; N. Reshetikhin; A. Schwarz; Y. Soibelman; C. Vafa; A.M. Vershik; N. Wallach; and S-T. Yau Nota de contenido: The Interaction between Geometry and Physics -- Uhlenbeck Spaces via Affine Lie Algebras -- New Questions Related to the Topological Degree -- Quantum Cobordisms and Formal Group Laws -- On the Foundations of Noncommutative Geometry -- Stable Distributions Supported on the Nilpotent Cone for the Group G 2 -- Infinite-Dimensional Vector Bundles in Algebraic Geometry -- Algebraic Lessons from the Theory of Quantum Integrable Models -- Affine Structures and Non-Archimedean Analytic Spaces -- Gelfand-Zeitlin Theory from the Perspective of Classical Mechanics. II -- Mirror Symmetry and Localizations -- Character Sheaves and Generalizations -- Symplectomorphism Groups and Quantum Cohomology -- Algebraic Structure of Yang-Mills Theory -- Seiberg-Witten Theory and Random Partitions -- Quantum Calabi-Yau and Classical Crystals -- Gelfand-Tsetlin Algebras, Expectations, Inverse Limits, Fourier Analysis En línea: http://dx.doi.org/10.1007/0-8176-4467-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34861 The Unity of Mathematics : In Honor of the Ninetieth Birthday of I.M. Gelfand [documento electrónico] / SpringerLink (Online service) ; Etingof, Pavel ; Retakh, Vladimir ; Singer, I. M . - Boston, MA : Birkhäuser Boston, 2006 . - XXII, 632 p. 41 illus : online resource. - (Progress in Mathematics; 244) .
ISBN : 978-0-8176-4467-3
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebraic geometry Group theory K-theory Topological groups Lie Geometry Physics Mathematical Methods in Groups, Groups K-Theory Theory and Generalizations Clasificación: 51 Matemáticas Resumen: A tribute to the vision and legacy of Israel Moiseevich Gelfand, the invited papers in this volume reflect the unity of mathematics as a whole, with particular emphasis on the many connections among the fields of geometry, physics, and representation theory. Written by leading mathematicians, the text is broadly divided into two sections: the first is devoted to developments at the intersection of geometry and physics, and the second to representation theory and algebraic geometry. Topics include conformal field theory, K-theory, noncommutative geometry, gauge theory, representations of infinite-dimensional Lie algebras, and various aspects of the Langlands program. Graduate students and researchers will benefit from and find inspiration in this broad and unique work, which brings together fundamental results in a number of disciplines and highlights the rewards of an interdisciplinary approach to mathematics and physics. Contributors: M. Atiyah; A. Braverman; H. Brezis; T. Coates; A. Connes; S. Debacker; V. Drinfeld; L.D. Faddeev; M. Finkelberg; D. Gaitsgory; I.M. Gelfand; A. Givental; D. Kazhdan; M. Kontsevich; B. Kostant; C-H. Liu; K. Liu; G. Lusztig; D. McDuff; M. Movshev; N.A. Nekrasov; A. Okounkov; N. Reshetikhin; A. Schwarz; Y. Soibelman; C. Vafa; A.M. Vershik; N. Wallach; and S-T. Yau Nota de contenido: The Interaction between Geometry and Physics -- Uhlenbeck Spaces via Affine Lie Algebras -- New Questions Related to the Topological Degree -- Quantum Cobordisms and Formal Group Laws -- On the Foundations of Noncommutative Geometry -- Stable Distributions Supported on the Nilpotent Cone for the Group G 2 -- Infinite-Dimensional Vector Bundles in Algebraic Geometry -- Algebraic Lessons from the Theory of Quantum Integrable Models -- Affine Structures and Non-Archimedean Analytic Spaces -- Gelfand-Zeitlin Theory from the Perspective of Classical Mechanics. II -- Mirror Symmetry and Localizations -- Character Sheaves and Generalizations -- Symplectomorphism Groups and Quantum Cohomology -- Algebraic Structure of Yang-Mills Theory -- Seiberg-Witten Theory and Random Partitions -- Quantum Calabi-Yau and Classical Crystals -- Gelfand-Tsetlin Algebras, Expectations, Inverse Limits, Fourier Analysis En línea: http://dx.doi.org/10.1007/0-8176-4467-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34861 Ejemplares
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Título : Topological Groups and Related Structures Tipo de documento: documento electrónico Autores: Alexander Arhangel’skii ; SpringerLink (Online service) ; Tkachenko, Mikhail Editorial: Paris : Atlantis Press Fecha de publicación: 2008 Colección: Atlantis Studies in Mathematics, ISSN 1875-7634 num. 1 Número de páginas: XIV, 781p Il.: online resource ISBN/ISSN/DL: 978-94-91216-35-0 Idioma : Inglés (eng) Palabras clave: Mathematics Group theory Algebraic topology Theory and Generalizations Topology Clasificación: 51 Matemáticas Resumen: Algebraandtopology,thetwofundamentaldomainsofmathematics,playcomplem- tary roles. Topology studies continuity and convergence and provides a general framework to study the concept of a limit. Much of topology is devoted to handling in?nite sets and in?nity itself; the methods developed are qualitative and, in a certain sense, irrational. - gebra studies all kinds of operations and provides a basis for algorithms and calculations. Very often, the methods here are ?nitistic in nature. Because of this difference in nature, algebra and topology have a strong tendency to develop independently, not in direct contact with each other. However, in applications, in higher level domains of mathematics, such as functional analysis, dynamical systems, representation theory, and others, topology and algebra come in contact most naturally. Many of the most important objects of mathematics represent a blend of algebraic and of topologicalstructures. Topologicalfunctionspacesandlineartopologicalspacesingeneral, topological groups and topological ?elds, transformation groups, topological lattices are objects of this kind. Very often an algebraic structure and a topology come naturally together; this is the case when they are both determined by the nature of the elements of the set considered (a group of transformations is a typical example). The rules that describe the relationship between a topology and an algebraic operation are almost always transparentandnatural—theoperationhastobecontinuous,jointlyorseparately Nota de contenido: to Topological Groups and Semigroups -- Right Topological and Semitopological Groups -- Topological groups: Basic constructions -- Some Special Classes of Topological Groups -- Cardinal Invariants of Topological Groups -- Moscow Topological Groups and Completions of Groups -- Free Topological Groups -- R-Factorizable Topological Groups -- Compactness and its Generalizations in Topological Groups -- Actions of Topological Groups on Topological Spaces En línea: http://dx.doi.org/10.2991/978-94-91216-35-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34446 Topological Groups and Related Structures [documento electrónico] / Alexander Arhangel’skii ; SpringerLink (Online service) ; Tkachenko, Mikhail . - Paris : Atlantis Press, 2008 . - XIV, 781p : online resource. - (Atlantis Studies in Mathematics, ISSN 1875-7634; 1) .
ISBN : 978-94-91216-35-0
Idioma : Inglés (eng)
Palabras clave: Mathematics Group theory Algebraic topology Theory and Generalizations Topology Clasificación: 51 Matemáticas Resumen: Algebraandtopology,thetwofundamentaldomainsofmathematics,playcomplem- tary roles. Topology studies continuity and convergence and provides a general framework to study the concept of a limit. Much of topology is devoted to handling in?nite sets and in?nity itself; the methods developed are qualitative and, in a certain sense, irrational. - gebra studies all kinds of operations and provides a basis for algorithms and calculations. Very often, the methods here are ?nitistic in nature. Because of this difference in nature, algebra and topology have a strong tendency to develop independently, not in direct contact with each other. However, in applications, in higher level domains of mathematics, such as functional analysis, dynamical systems, representation theory, and others, topology and algebra come in contact most naturally. Many of the most important objects of mathematics represent a blend of algebraic and of topologicalstructures. Topologicalfunctionspacesandlineartopologicalspacesingeneral, topological groups and topological ?elds, transformation groups, topological lattices are objects of this kind. Very often an algebraic structure and a topology come naturally together; this is the case when they are both determined by the nature of the elements of the set considered (a group of transformations is a typical example). The rules that describe the relationship between a topology and an algebraic operation are almost always transparentandnatural—theoperationhastobecontinuous,jointlyorseparately Nota de contenido: to Topological Groups and Semigroups -- Right Topological and Semitopological Groups -- Topological groups: Basic constructions -- Some Special Classes of Topological Groups -- Cardinal Invariants of Topological Groups -- Moscow Topological Groups and Completions of Groups -- Free Topological Groups -- R-Factorizable Topological Groups -- Compactness and its Generalizations in Topological Groups -- Actions of Topological Groups on Topological Spaces En línea: http://dx.doi.org/10.2991/978-94-91216-35-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34446 Ejemplares
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Título : Self-Dual Codes and Invariant Theory Tipo de documento: documento electrónico Autores: Nebe, Gabriele ; SpringerLink (Online service) ; Rains, Eric M ; Sloane, Neil J.A Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2006 Colección: Algorithms and Computation in Mathematics, ISSN 1431-1550 num. 17 Número de páginas: XXIV, 406 p Il.: online resource ISBN/ISSN/DL: 978-3-540-30731-0 Idioma : Inglés (eng) Palabras clave: Mathematics Coding theory Algebra Group Number Quantum physics Control engineering Robotics Mechatronics and Information Theory Generalizations Control, Robotics, Physics Clasificación: 51 Matemáticas Resumen: One of the most remarkable and beautiful theorems in coding theory is Gleason's 1970 theorem about the weight enumerators of self-dual codes and their connections with invariant theory. In the past 35 years there have been hundreds of papers written about generalizations and applications of this theorem to different types of codes. This self-contained book develops a new theory which is powerful enough to include all the earlier generalizations. It is also in part an encyclopedia that gives a very extensive list of the different types of self-dual codes and their properties, including tables of the best codes that are presently known. Besides self-dual codes, the book also discusses two closely-related subjects, lattices and modular forms, and quantum error-correcting codes. This book, written by the leading experts in the subject, has no equivalent in the literature and will be of great interest to mathematicians, communication theorists, computer scientists and physicists Nota de contenido: The Type of a Self-Dual Code -- Weight Enumerators and Important Types -- Closed Codes -- The Category Quad -- The Main Theorems -- Real and Complex Clifford Groups -- Classical Self-Dual Codes -- Further Examples of Self-Dual Codes -- Lattices -- Maximal Isotropic Codes and Lattices -- Extremal and Optimal Codes -- Enumeration of Self-Dual Codes -- Quantum Codes En línea: http://dx.doi.org/10.1007/3-540-30731-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34927 Self-Dual Codes and Invariant Theory [documento electrónico] / Nebe, Gabriele ; SpringerLink (Online service) ; Rains, Eric M ; Sloane, Neil J.A . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2006 . - XXIV, 406 p : online resource. - (Algorithms and Computation in Mathematics, ISSN 1431-1550; 17) .
ISBN : 978-3-540-30731-0
Idioma : Inglés (eng)
Palabras clave: Mathematics Coding theory Algebra Group Number Quantum physics Control engineering Robotics Mechatronics and Information Theory Generalizations Control, Robotics, Physics Clasificación: 51 Matemáticas Resumen: One of the most remarkable and beautiful theorems in coding theory is Gleason's 1970 theorem about the weight enumerators of self-dual codes and their connections with invariant theory. In the past 35 years there have been hundreds of papers written about generalizations and applications of this theorem to different types of codes. This self-contained book develops a new theory which is powerful enough to include all the earlier generalizations. It is also in part an encyclopedia that gives a very extensive list of the different types of self-dual codes and their properties, including tables of the best codes that are presently known. Besides self-dual codes, the book also discusses two closely-related subjects, lattices and modular forms, and quantum error-correcting codes. This book, written by the leading experts in the subject, has no equivalent in the literature and will be of great interest to mathematicians, communication theorists, computer scientists and physicists Nota de contenido: The Type of a Self-Dual Code -- Weight Enumerators and Important Types -- Closed Codes -- The Category Quad -- The Main Theorems -- Real and Complex Clifford Groups -- Classical Self-Dual Codes -- Further Examples of Self-Dual Codes -- Lattices -- Maximal Isotropic Codes and Lattices -- Extremal and Optimal Codes -- Enumeration of Self-Dual Codes -- Quantum Codes En línea: http://dx.doi.org/10.1007/3-540-30731-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34927 Ejemplares
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