Quantum Affine Algebras, Extended Affine Lie Algebras, and Their Applications

Quantum Affine Algebras, Extended Affine Lie Algebras, and Applications, March 2-7, 2008, Banff International Research Station, Banff, Canada

Author: Yun Gao

Publisher: American Mathematical Soc.

ISBN: 0821845071

Category: Mathematics

Page: 302

View: 4636

This volume contains the proceedings of the conference on Quantum Affine Algebras, Extended Affine Lie Algebras, and Applications, which was held at the Banff International Research Station, Banff, Canada, from March 2-7, 2008. Many of the papers include new results on different aspects of quantum affine algebras, extended affine Lie algebras, and their applications in other areas of mathematics and physics. Any reader interested in learning about the recent developments in quantum affine algebras and extended affine Lie algebras will benefit from this book.
Posted in Mathematics

Recent Developments in Quantum Affine Algebras and Related Topics

Representations of Affine and Quantum Affine Algebras and Their Applications, North Carolina State University, May 21-24, 1998

Author: Naihuan Jing,Kailash C. Misra

Publisher: American Mathematical Soc.

ISBN: 0821811991

Category: Mathematics

Page: 469

View: 5324

This volume reflects the proceedings of the International Conference on Representations of Affine and Quantum Affine Algebras and Their Applications held at North Carolina State University (Raleigh). In recent years, the theory of affine and quantum affine Lie algebras has become an important area of mathematical research with numerous applications in other areas of mathematics and physics. Three areas of recent progress are the focus of this volume: affine and quantum affine algebras and their generalizations, vertex operator algebras and their representations, and applications in combinatorics and statistical mechanics. Talks given by leading international experts at the conference offered both overviews on the subjects and current research results. The book nicely presents the interplay of these topics recently occupying 'center stage' in the theory of infinite dimensional Lie theory.
Posted in Mathematics

Recent Developments in Quantum Affine Algebras and Related Topics

Representations of Affine and Quantum Affine Algebras and Their Applications, North Carolina State University, May 21-24, 1998

Author: Naihuan Jing,Kailash C. Misra

Publisher: American Mathematical Soc.

ISBN: 0821811991

Category: Mathematics

Page: 469

View: 2431

This volume reflects the proceedings of the International Conference on Representations of Affine and Quantum Affine Algebras and Their Applications held at North Carolina State University (Raleigh). In recent years, the theory of affine and quantum affine Lie algebras has become an important area of mathematical research with numerous applications in other areas of mathematics and physics. Three areas of recent progress are the focus of this volume: affine and quantum affine algebras and their generalizations, vertex operator algebras and their representations, and applications in combinatorics and statistical mechanics. Talks given by leading international experts at the conference offered both overviews on the subjects and current research results. The book nicely presents the interplay of these topics recently occupying 'center stage' in the theory of infinite dimensional Lie theory.
Posted in Mathematics

Representations of Lie Algebras, Quantum Groups and Related Topics

Author: Naihuan Jing,Kailash C. Misra

Publisher: American Mathematical Soc.

ISBN: 1470436965

Category: Algebra

Page: 233

View: 2667

This volume contains the proceedings of the AMS Special Session on Representations of Lie Algebras, Quantum Groups and Related Topics, held from November 12–13, 2016, at North Carolina State University, Raleigh, North Carolina. The articles cover various aspects of representations of Kac–Moody Lie algebras and their applications, structure of Leibniz algebras and Krichever–Novikov algebras, representations of quantum groups, and related topics.
Posted in Algebra

Symmetries, Integrable Systems and Representations

Author: Kenji Iohara,Sophie Morier-Genoud,Bertrand Rémy

Publisher: Springer Science & Business Media

ISBN: 1447148630

Category: Mathematics

Page: 638

View: 4224

This volume is the result of two international workshops; Infinite Analysis 11 – Frontier of Integrability – held at University of Tokyo, Japan in July 25th to 29th, 2011, and Symmetries, Integrable Systems and Representations held at Université Claude Bernard Lyon 1, France in December 13th to 16th, 2011. Included are research articles based on the talks presented at the workshops, latest results obtained thereafter, and some review articles. The subjects discussed range across diverse areas such as algebraic geometry, combinatorics, differential equations, integrable systems, representation theory, solvable lattice models and special functions. Through these topics, the reader will find some recent developments in the field of mathematical physics and their interactions with several other domains.
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Recent Developments in Algebraic and Combinatorial Aspects of Representation Theory

Author: Vyjayanthi Chari,Jacob Greenstein,Kailash C. Misra,K. N. Raghavan,Sankaran Viswanath

Publisher: American Mathematical Soc.

ISBN: 0821890379

Category: Mathematics

Page: 210

View: 5034

This volume contains the proceedings of the International Congress of Mathematicians Satellite Conference on Algebraic and Combinatorial Approaches to Representation Theory, held August 12-16, 2010, at the National Institute of Advanced Studies, Bangalore, India, and the follow-up conference held May 18-20, 2012, at the University of California, Riverside, CA. It contains original research and survey articles on various topics in the theory of representations of Lie algebras, quantum groups and algebraic groups, including crystal bases, categorification, toroidal algebras and their generalizations, vertex algebras, Hecke algebras, Kazhdan-Lusztig bases, $q$-Schur algebras, and Weyl algebras.
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Recent Developments in Infinite-dimensional Lie Algebras and Conformal Field Theory

Proceedings of an International Conference on Infinite-dimensional Lie Theory and Conformal Field Theory, May 23-27, 2000, University of Virginia, Charlottesville, Virginia

Author: Stephen Berman

Publisher: American Mathematical Soc.

ISBN: 9780821856338

Category: Mathematics

Page: 334

View: 8168

Because of its many applications to mathematics and mathematical physics, the representation theory of infinite-dimensional Lie and quantized enveloping algebras comprises an important area of current research. This volume includes articles from the proceedings of an international conference, ''Infinite-Dimensional Lie Theory and Conformal Field Theory'', held at the University of Virginia. Many of the contributors to the volume are prominent researchers in the field. Thisconference provided an opportunity for mathematicians and physicists to interact in an active research area of mutual interest. The talks focused on recent developments in the representation theory of affine, quantum affine, and extended affine Lie algebras and Lie superalgebras. They also highlightedapplications to conformal field theory, integrable and disordered systems. Some of the articles are expository and accessible to a broad readership of mathematicians and physicists interested in this area; others are research articles that are appropriate for more advanced readers.
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Affine Lie Algebras and Quantum Groups

An Introduction, with Applications in Conformal Field Theory

Author: Jürgen Fuchs

Publisher: Cambridge University Press

ISBN: 9780521484121

Category: Mathematics

Page: 433

View: 4748

This is an introduction to the theory of affine Lie algebras and to the theory of quantum groups. It is unique in discussing these two subjects in a unified manner, which is made possible by discussing their respective applications in conformal field theory. The description of affine algebras covers the classification problem, the connection with loop algebras, and representation theory including modular properties. The necessary background from the theory of semisimple Lie algebras is also provided. The discussion of quantum groups concentrates on deformed enveloping algebras and their representation theory, but other aspects such as R-matrices and matrix quantum groups are also dealt with.
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The Monster and Lie Algebras

Proceedings of a Special Research Quarter at the Ohio State University, May 1996

Author: Joseph Ferrar,Koichiro Harada

Publisher: Walter de Gruyter

ISBN: 3110801892

Category: Mathematics

Page: 262

View: 1602

This series is devoted to the publication of monographs, lecture resp. seminar notes, and other materials arising from programs of the OSU Mathemaical Research Institute. This includes proceedings of conferences or workshops held at the Institute, and other mathematical writings.
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Geometric Representation Theory and Extended Affine Lie Algebras

Author: Erhard Neher,Alistair Savage,Weiqiang Wang

Publisher: American Mathematical Soc.

ISBN: 0821871617

Category: Mathematics

Page: 213

View: 3595

This text presents lectures given at the Fields Institute Summer School on Geometric Representation Theory and Extended Affine Lie Algebras held at the University of Ottawa in 2009. It provides a systematic account by experts of some of the developments in Lie algebras and representation theory in the last two decades.
Posted in Mathematics

Kac-Moody Lie Algebras and Related Topics

Ramanujan International Symposium on Kac-Moody Lie Algebras and Applications, January 28-31, 2002, Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai, India

Author: Neelacanta Sthanumoorthy,Kailash C. Misra

Publisher: American Mathematical Soc.

ISBN: 0821833375

Category: Mathematics

Page: 370

View: 5127

This volume is the proceedings of the Ramanujan International Symposium on Kac-Moody Lie algebras and their applications. The symposium provided researchers in mathematics and physics with the opportunity to discuss new developments in this rapidly-growing area of research. The book contains several excellent articles with new and significant results. It is suitable for graduate students and researchers working in Kac-Moody Lie algebras, their applications, and related areas of research.
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Infinite Dimensional Groups and Algebras in Quantum Physics

Author: Johnny T. Ottesen

Publisher: Springer Science & Business Media

ISBN: 3540589147

Category: Science

Page: 218

View: 2194

The idea of writing this book appeared when I was working on some problems related to representations of physically relevant infinite - mensional groups of operators on physically relevant Hilbert spaces. The considerations were local, reducing the subject to dealing with representations of infinite-dimensional Lie algebras associated with the associated groups. There is a large number of specialized articles and books on parts of this subject, but to our suprise only a few represent the point of view given in this book. Moreover, none of the written material was self-contained. At present, the subject has not reached its final form and active research is still being undertaken. I present this subject of growing importance in a unified manner and by a fairly simple approach. I present a route by which students can absorb and understand the subject, only assuming that the reader is familliar with functional analysis, especially bounded and unbounded operators on Hilbert spaces. Moreover, I assume a little basic knowledge of algebras , Lie algebras, Lie groups, and manifolds- at least the definitions. The contents are presented in detail in the introduction in Chap. The manuscript of this book has been succesfully used by some advanced graduate students at Aarhus University, Denmark, in their "A-exame'. I thank them for comments.
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Lie Groups, Lie Algebras, Cohomology and Some Applications in Physics

Author: Josi A. de Azcárraga,Josi M. Izquierdo

Publisher: Cambridge University Press

ISBN: 9780521597005

Category: Mathematics

Page: 455

View: 1975

Now in paperback, this book provides a self-contained introduction to the cohomology theory of Lie groups and algebras and to some of its applications in physics. No previous knowledge of the mathematical theory is assumed beyond some notions of Cartan calculus and differential geometry (which are nevertheless reviewed in the book in detail). The examples, of current interest, are intended to clarify certain mathematical aspects and to show their usefulness in physical problems. The topics treated include the differential geometry of Lie groups, fibre bundles and connections, characteristic classes, index theorems, monopoles, instantons, extensions of Lie groups and algebras, some applications in supersymmetry, Chevalley-Eilenberg approach to Lie algebra cohomology, symplectic cohomology, jet-bundle approach to variational principles in mechanics, Wess-Zumino-Witten terms, infinite Lie algebras, the cohomological descent in mechanics and in gauge theories and anomalies. This book will be of interest to graduate students and researchers in theoretical physics and applied mathematics.
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Affine Lie Algebras, Weight Multiplicities, and Branching Rules

Author: Sam Kass,R. V. Moody,J. Patera,R. Slansky

Publisher: Univ of California Press

ISBN: 9780520067684

Category: Science

Page: 893

View: 6367

00 This practical treatise is an introduction to the mathematics and physics of affine Kac-Moody algebras. It is the result of an unusual interdisciplinary effort by two physicists and two mathematicians to make this field understandable to a broad readership and to illuminate the connections among seemingly disparate domains of mathematics and physics that are tantalizingly suggested by the ubiquity of Lie theory. The book will be useful to Lie algebraists, high energy physicists, statistical mechanics, and number theorists. Volume One contains a description of Kac-Moody Lie algebras, and especially the affine algebras and their representations; the results of extensive computations follow in Volume Two, which is spiral bound for easy reference. This practical treatise is an introduction to the mathematics and physics of affine Kac-Moody algebras. It is the result of an unusual interdisciplinary effort by two physicists and two mathematicians to make this field understandable to a broad readership and to illuminate the connections among seemingly disparate domains of mathematics and physics that are tantalizingly suggested by the ubiquity of Lie theory. The book will be useful to Lie algebraists, high energy physicists, statistical mechanics, and number theorists. Volume One contains a description of Kac-Moody Lie algebras, and especially the affine algebras and their representations; the results of extensive computations follow in Volume Two, which is spiral bound for easy reference.
Posted in Science

Kac-Moody Groups, their Flag Varieties and Representation Theory

Author: Shrawan Kumar

Publisher: Springer Science & Business Media

ISBN: 9780817642273

Category: Mathematics

Page: 606

View: 6170

This is the first monograph to exclusively treat Kac-Moody (K-M) groups, a standard tool in mathematics and mathematical physics. K-M Lie algebras were introduced in the mid-sixties independently by V. Kac and R. Moody, generalizing finite-dimensional semisimple Lie algebras. K-M theory has since undergone tremendous developments in various directions and has profound connections with a number of diverse areas, including number theory, combinatorics, topology, singularities, quantum groups, completely integrable systems, and mathematical physics. This comprehensive, well-written text moves from K-M Lie algebras to the broader K-M Lie group setting, and focuses on the study of K-M groups and their flag varieties. In developing K-M theory from scratch, the author systematically leads readers to the forefront of the subject, treating the algebro-geometric, topological, and representation-theoretic aspects of the theory. Most of the material presented here is not available anywhere in the book literature. {\it Kac--Moody Groups, their Flag Varieties and Representation Theory} is suitable for an advanced graduate course in representation theory, and contains a number of examples, exercises, challenging open problems, comprehensive bibliography, and index. Research mathematicians at the crossroads of representation theory, geometry, and topology will learn a great deal from this text; although the book is devoted to the general K-M case, those primarily interested in the finite-dimensional case will also benefit. No prior knowledge of K-M Lie algebras or of (finite-dimensional) algebraic groups is required, but some basic knowledge would certainly be helpful. For the reader's convenience some of the basic results needed from other areas, including ind-varieties, pro-algebraic groups and pro-Lie algebras, Tits systems, local cohomology, equivariant cohomology, and homological algebra are included.
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Introduction to Vertex Operator Algebras and Their Representations

Author: James Lepowsky,Haisheng Li

Publisher: Springer Science & Business Media

ISBN: 0817681868

Category: Mathematics

Page: 318

View: 2986

* Introduces the fundamental theory of vertex operator algebras and its basic techniques and examples. * Begins with a detailed presentation of the theoretical foundations and proceeds to a range of applications. * Includes a number of new, original results and brings fresh perspective to important works of many other researchers in algebra, lie theory, representation theory, string theory, quantum field theory, and other areas of math and physics.
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Lie Algebras, Part 2

Finite and Infinite Dimensional Lie Algebras and Applications in Physics

Author: E.A. de Kerf,G.G.A. Bäuerle,A.P.E. ten Kroode

Publisher: Elsevier

ISBN: 9780080535463

Category: Science

Page: 553

View: 6225

This is the long awaited follow-up to Lie Algebras, Part I which covered a major part of the theory of Kac-Moody algebras, stressing primarily their mathematical structure. Part II deals mainly with the representations and applications of Lie Algebras and contains many cross references to Part I. The theoretical part largely deals with the representation theory of Lie algebras with a triangular decomposition, of which Kac-Moody algebras and the Virasoro algebra are prime examples. After setting up the general framework of highest weight representations, the book continues to treat topics as the Casimir operator and the Weyl-Kac character formula, which are specific for Kac-Moody algebras. The applications have a wide range. First, the book contains an exposition on the role of finite-dimensional semisimple Lie algebras and their representations in the standard and grand unified models of elementary particle physics. A second application is in the realm of soliton equations and their infinite-dimensional symmetry groups and algebras. The book concludes with a chapter on conformal field theory and the importance of the Virasoro and Kac-Moody algebras therein.
Posted in Science

Publications Update

Author: World Bank

Publisher: N.A

ISBN: N.A

Category:

Page: N.A

View: 3422

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Representation Theory and Noncommutative Harmonic Analysis I

Fundamental Concepts. Representations of Virasoro and Affine Algebras

Author: Alexandre Kirillov

Publisher: Springer Science & Business Media

ISBN: 9783540186984

Category: Mathematics

Page: 236

View: 8191

This two-part survey provides a short review of the classical part of representation theory, carefully exposing the structure of the theory without overwhelming readers with details, and deals with representations of Virasoro and Kac-Moody algebra. It presents a wealth of recent results on representations of infinite-dimensional groups.
Posted in Mathematics