Recent Developments In Infinite Dimensional Lie Algebras And Conformal Field Theory

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Recent Developments in Infinite-Dimensional Lie Algebras and Conformal Field Theory

Stephen Berman,Paul Fendley,Yi-Zhi Huang,Kailash Misra,Brian Parshall
Recent Developments in Infinite Dimensional Lie Algebras and Conformal Field Theory Book PDF

Author : Stephen Berman,Paul Fendley,Yi-Zhi Huang,Kailash Misra,Brian Parshall
Publisher : American Mathematical Soc.
Page : 346 pages
File Size : 47,5 Mb
Release : 2002
Category : Conformal invariants
ISBN : 9780821827161

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Recent Developments in Infinite-Dimensional Lie Algebras and Conformal Field Theory by Stephen Berman,Paul Fendley,Yi-Zhi Huang,Kailash Misra,Brian Parshall Pdf

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.

Developments and Trends in Infinite-Dimensional Lie Theory

Karl-Hermann Neeb,Arturo Pianzola
Developments and Trends in Infinite Dimensional Lie Theory Book PDF

Author : Karl-Hermann Neeb,Arturo Pianzola
Publisher : Springer Science & Business Media
Page : 492 pages
File Size : 44,6 Mb
Release : 2010-10-17
Category : Mathematics
ISBN : 9780817647414

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Developments and Trends in Infinite-Dimensional Lie Theory by Karl-Hermann Neeb,Arturo Pianzola Pdf

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. Contributors: B. Allison, D. Beltiţă, 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.

Infinite Dimensional Lie Groups in Geometry and Representation Theory

Augustin Banyaga,Joshua A Leslie,Thierry Robart
Infinite Dimensional Lie Groups in Geometry and Representation Theory Book PDF

Author : Augustin Banyaga,Joshua A Leslie,Thierry Robart
Publisher : World Scientific
Page : 176 pages
File Size : 48,6 Mb
Release : 2002-07-12
Category : Science
ISBN : 9789814488143

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Infinite Dimensional Lie Groups in Geometry and Representation Theory by Augustin Banyaga,Joshua A Leslie,Thierry Robart Pdf

This book constitutes the proceedings of the 2000 Howard conference on “Infinite Dimensional Lie Groups in Geometry and Representation Theory”. It presents some important recent developments in this area. It opens with a topological characterization of regular groups, treats among other topics the integrability problem of various infinite dimensional Lie algebras, presents substantial contributions to important subjects in modern geometry, and concludes with interesting applications to representation theory. The book should be a new source of inspiration for advanced graduate students and established researchers in the field of geometry and its applications to mathematical physics. Contents:Inheritance Properties for Lipschitz-Metrizable Frölicher Groups (J Teichmann)Around the Exponential Mapping (T Robart)On a Solution to a Global Inverse Problem with Respect to Certain Generalized Symmetrizable Kac-Moody Algebras (J A Leslie)The Lie Group of Fourier Integral Operators on Open Manifolds (R Schmid)On Some Properties of Leibniz Algebroids (A Wade)On the Geometry of Locally Conformal Symplectic Manifolds (A Banyaga)Some Properties of Locally Conformal Symplectic Manifolds (S Haller)Criticality of Unit Contact Vector Fields (P Rukimbira)Orbifold Homeomorphism and Diffeomorphism Groups (J E Borzellino & V Brunsden)A Note on Isotopies of Symplectic and Poisson Structures (A Banyaga & P Donato)Remarks on Actions on Compacta by Some Infinite-Dimensional Groups (V Pestov) Readership: Graduate students and researchers in mathematics and mathematical physics. Keywords:

Current Algebras on Riemann Surfaces

Oleg K. Sheinman
Current Algebras on Riemann Surfaces Book PDF

Author : Oleg K. Sheinman
Publisher : Walter de Gruyter
Page : 164 pages
File Size : 45,9 Mb
Release : 2012-10-01
Category : Mathematics
ISBN : 9783110264524

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Current Algebras on Riemann Surfaces by Oleg K. Sheinman Pdf

This monograph is an introduction into a new and fast developing field on the crossroads of infinite-dimensional Lie algebra theory and contemporary mathematical physics. It contains a self-consistent presentation of the theory of Krichever-Novikov algebras, Lax operator algebras, their interaction, representation theory, relations to moduli spaces of Riemann surfaces and holomorphic vector bundles on them, to Lax integrable systems, and conformal field theory. For beginners, the book provides a short way to join in the investigations in these fields. For experts, it sums up the recent advances in the theory of almost graded infinite-dimensional Lie algebras and their applications. The book may serve as a base for semester lecture courses on finite-dimensional integrable systems, conformal field theory, almost graded Lie algebras. Majority of results are presented for the first time in the form of monograph.

Recent Developments in Lie Algebras, Groups, and Representation Theory

Kailash C. Misra,Daniel Ken Nakano,Brian Parshall
Recent Developments in Lie Algebras Groups and Representation Theory Book PDF

Author : Kailash C. Misra,Daniel Ken Nakano,Brian Parshall
Publisher : American Mathematical Soc.
Page : 310 pages
File Size : 55,8 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821869178

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Recent Developments in Lie Algebras, Groups, and Representation Theory by Kailash C. Misra,Daniel Ken Nakano,Brian Parshall Pdf

This book contains the proceedings of the 2009-2011 Southeastern Lie Theory Workshop Series, held October 9-11, 2009 at North Carolina State University, May 22-24, 2010, at the University of Georgia, and June 1-4, 2011 at the University of Virginia. Some of the articles, written by experts in the field, survey recent developments while others include new results in Lie algebras, quantum groups, finite groups, and algebraic groups.

Conformal Field Theories and Tensor Categories

Chengming Bai,Jürgen Fuchs,Yi-Zhi Huang,Liang Kong,Ingo Runkel,Christoph Schweigert
Conformal Field Theories and Tensor Categories Book PDF

Author : Chengming Bai,Jürgen Fuchs,Yi-Zhi Huang,Liang Kong,Ingo Runkel,Christoph Schweigert
Publisher : Springer Science & Business Media
Page : 279 pages
File Size : 50,9 Mb
Release : 2013-10-30
Category : Mathematics
ISBN : 9783642393839

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Conformal Field Theories and Tensor Categories by Chengming Bai,Jürgen Fuchs,Yi-Zhi Huang,Liang Kong,Ingo Runkel,Christoph Schweigert Pdf

The present volume is a collection of seven papers that are either based on the talks presented at the workshop "Conformal field theories and tensor categories" held June 13 to June 17, 2011 at the Beijing International Center for Mathematical Research, Peking University, or are extensions of the material presented in the talks at the workshop. These papers present new developments beyond rational conformal field theories and modular tensor categories and new applications in mathematics and physics. The topics covered include tensor categories from representation categories of Hopf algebras, applications of conformal field theories and tensor categories to topological phases and gapped systems, logarithmic conformal field theories and the corresponding non-semisimple tensor categories, and new developments in the representation theory of vertex operator algebras. Some of the papers contain detailed introductory material that is helpful for graduate students and researchers looking for an introduction to these research directions. The papers also discuss exciting recent developments in the area of conformal field theories, tensor categories and their applications and will be extremely useful for researchers working in these areas.

Lie Algebras, Part 2

E.A. de Kerf,G.G.A. Bäuerle,A.P.E. ten Kroode
Lie Algebras Part 2 Book PDF

Author : E.A. de Kerf,G.G.A. Bäuerle,A.P.E. ten Kroode
Publisher : Elsevier
Page : 553 pages
File Size : 49,7 Mb
Release : 1997-10-30
Category : Science
ISBN : 0080535461

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Lie Algebras, Part 2 by E.A. de Kerf,G.G.A. Bäuerle,A.P.E. ten Kroode Pdf

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.

Recent Developments in Quantum Affine Algebras and Related Topics

Naihuan Jing,Kailash C. Misra
Recent Developments in Quantum Affine Algebras and Related Topics Book PDF

Author : Naihuan Jing,Kailash C. Misra
Publisher : American Mathematical Soc.
Page : 482 pages
File Size : 52,8 Mb
Release : 1999
Category : Affine algebraic groups
ISBN : 9780821811993

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Recent Developments in Quantum Affine Algebras and Related Topics by Naihuan Jing,Kailash C. Misra Pdf

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 "centre stage" in the theory of infinite dimensional Lie theory.

Lie Algebras, Lie Superalgebras, Vertex Algebras and Related Topics

Kailash C. Misra,Daniel K. Nakano,Brian J. Parshall
Lie Algebras Lie Superalgebras Vertex Algebras and Related Topics Book PDF

Author : Kailash C. Misra,Daniel K. Nakano,Brian J. Parshall
Publisher : American Mathematical Soc.
Page : 355 pages
File Size : 43,8 Mb
Release : 2016-06-28
Category : Group theory and generalizations
ISBN : 9781470418441

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Lie Algebras, Lie Superalgebras, Vertex Algebras and Related Topics by Kailash C. Misra,Daniel K. Nakano,Brian J. Parshall Pdf

This book contains the proceedings of the 2012–2014 Southeastern Lie Theory Workshop Series held at North Carolina State University in April 2012, at College of Charleston in December 2012, at Louisiana State University in May 2013, and at University of Georgia in May 2014. Some of the articles by experts in the field survey recent developments while others include new results in representations of Lie algebras, and quantum groups, vertex (operator) algebras and Lie superalgebras.

Finite and Infinite Dimensional Analysis in Honor of Leonard Gross

Analysis on Infinit Ams Special Session,Hui-Hsiung Kuo,Ambar Sengupta
Finite and Infinite Dimensional Analysis in Honor of Leonard Gross Book PDF

Author : Analysis on Infinit Ams Special Session,Hui-Hsiung Kuo,Ambar Sengupta
Publisher : American Mathematical Soc.
Page : 224 pages
File Size : 53,8 Mb
Release : 2003
Category : Mathematics
ISBN : 9780821832028

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Finite and Infinite Dimensional Analysis in Honor of Leonard Gross by Analysis on Infinit Ams Special Session,Hui-Hsiung Kuo,Ambar Sengupta Pdf

This book contains the proceedings of the special session in honor of Leonard Gross held at the annual Joint Mathematics Meetings in New Orleans (LA). The speakers were specialists in a variety of fields, and many were Professor Gross' former Ph.D. students and their descendants. Papers in this volume present results from several areas of mathematics. They illustrate applications of powerful ideas that originated in Gross' work and permeate diverse fields. Topics of this title include stochastic partial differential equations, white noise analysis, Brownian motion, Segal-Bargmann analysis, heat kernels, and some applications. The volume should be useful to graduate students and researchers. It provides perspective on current activity and on central ideas and techniques in the topics covered.

Infinite Dimensional Lie Algebras and Groups

V G Kac
Infinite Dimensional Lie Algebras and Groups Book PDF

Author : V G Kac
Publisher : World Scientific
Page : 640 pages
File Size : 42,5 Mb
Release : 1989-07-01
Category : Electronic
ISBN : 9789814663175

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Infinite Dimensional Lie Algebras and Groups by V G Kac Pdf

Contents:Integrable Representation of Kac-Moody Algebras: Results and Open Problems (V Chari & A Pressley)Existence of Certain Components in the Tensor Product of Two Integrable Highest Weight Modules for Kac-Moody Algebras (SKumar)Frobenius Action on the B-Cohomology (O Mathieu)Certain Rank Two Subsystems of Kac-Moody Root Systems (J Morita)Lie Groups Associated to Kac-Moody Lie Algebras: An Analytic Approach (E Rodriguez-Carrington)Almost Split-K-Forms of Kac-Moody Algebras (G Rousseau)Global Representations of the Diffeomorphism Groups of the Circle (F Bien)Path Space Realization of the Basic Representation of An(1) (E Date et al)Boson-Fermion Correspondence Over (C De Concini et al)Classification of Modular Invariant Representations of Affine Algebras (V G Kac & M Wakimoto)Standard Monomial Theory for SL2 (V Lakshmibai & C S Seshadri)Some Results on Modular Invariant Representations (S Lu)Current Algebras in 3+1 Space-Time Dimensions (J Mickelson)Standard Representations of An(1) (M Primc)Representations of the Algebra Uq(sI(2)), q-Orthogonal Polynomials and Invariants of Links (A N Kirillov & N Yu Reshetikhin)Infinite Super Grassmannians and Super Plücker Equations (M J Bergvelt)Drinfeld-Sokolov Hierarchies and t-Functions (H J Imbens)Super Boson-Fermion Correspondence of Type B (V G Kac & J W van de Leur)Prym Varieties and Soliton Equations (T Shiota)Polynomial Solutions of the BKP Hierarchy and Projective Representations of Symmetric Groups (Y You)Toward Generalized Macdonald's Identities (D Bernard)Conformal Theories with Non-Linearly Extended Virasoro Symmetries and Lie Algebra Classification (A Bilal & J-LGervais)Extended Conformal Algebras from Kac-Moody Algebras (P Bouwknegt)Meromorphic Conformal Field Theory (P Goddard)Local Extensions of the U(1) Current Algebra and Their Positive Energy Representations (R R Paunov & I T Todorov)Conformal Field Theory on Moduli Family of Stable Curves with Gauge Symmetries (A Tsuchiya & Y Yamada) Readership: Mathematicians and mathematical physicists

Infinite-dimensional Aspects of Representation Theory and Applications

Stephen Berman
Infinite dimensional Aspects of Representation Theory and Applications Book PDF

Author : Stephen Berman
Publisher : American Mathematical Soc.
Page : 154 pages
File Size : 54,7 Mb
Release : 2005
Category : Mathematics
ISBN : 9780821837016

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Infinite-dimensional Aspects of Representation Theory and Applications by Stephen Berman Pdf

The University of Virginia (Charlottesville) hosted an international conference on Infinite-dimensional Aspects of Representation Theory and Applications. This volume contains papers resulting from the mini-courses and talks given at the meeting. Beyond the techniques and ideas related to representation theory, the book demonstrates connections to number theory, algebraic geometry, and mathematical physics. The specific topics covered include Hecke algebras, quantum groups, infinite-dimensional Lie algebras, quivers, modular representations, and Gromov-Witten invariants. The book is suitable for graduate students and researchers interested in representation theory.

Advances in Lie Superalgebras

Maria Gorelik,Paolo Papi
Advances in Lie Superalgebras Book PDF

Author : Maria Gorelik,Paolo Papi
Publisher : Springer Science & Business
Page : 280 pages
File Size : 51,5 Mb
Release : 2014-04-28
Category : Mathematics
ISBN : 9783319029528

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Advances in Lie Superalgebras by Maria Gorelik,Paolo Papi Pdf

The volume is the outcome of the conference "Lie superalgebras," which was held at the Istituto Nazionale di Alta Matematica, in 2012. The conference gathered many specialists in the subject, and the talks held provided comprehensive insights into the newest trends in research on Lie superalgebras (and related topics like vertex algebras, representation theory and supergeometry). The book contains contributions of many leading esperts in the field and provides a complete account of the newest trends in research on Lie Superalgebras.

Introduction to Vertex Operator Algebras and Their Representations

James Lepowsky,Haisheng Li
Introduction to Vertex Operator Algebras and Their Representations Book PDF

Author : James Lepowsky,Haisheng Li
Publisher : Springer Science & Business Media
Page : 330 pages
File Size : 40,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9780817681869

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Introduction to Vertex Operator Algebras and Their Representations by James Lepowsky,Haisheng Li Pdf

* 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.

Krichever–Novikov Type Algebras

Martin Schlichenmaier
Krichever Novikov Type Algebras Book PDF

Author : Martin Schlichenmaier
Publisher : Walter de Gruyter GmbH & Co KG
Page : 375 pages
File Size : 48,5 Mb
Release : 2014-08-19
Category : Mathematics
ISBN : 9783110279641

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Krichever–Novikov Type Algebras by Martin Schlichenmaier Pdf

Krichever and Novikov introduced certain classes of infinite dimensionalLie algebrasto extend the Virasoro algebra and its related algebras to Riemann surfaces of higher genus. The author of this book generalized and extended them toa more general setting needed by the applications. Examples of applications are Conformal Field Theory, Wess-Zumino-Novikov-Witten models, moduli space problems, integrable systems, Lax operator algebras, and deformation theory of Lie algebra. Furthermore they constitute an important class of infinite dimensional Lie algebras which due to their geometric origin are still manageable. This book gives an introduction for the newcomer to this exciting field of ongoing research in mathematics and will be a valuable source of reference for the experienced researcher. Beside the basic constructions and results also applications are presented.