Lie Algebras Vertex Operator Algebras And Related Topics

Author : Katrina Barron
Publisher : American Mathematical Soc.
ISBN 13 : 1470426668
Total Pages : 274 pages
Book Rating : 4.68/5 ( download)

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Download or read book Lie Algebras, Vertex Operator Algebras, and Related Topics written by Katrina Barron and published by American Mathematical Soc.. This book was released on 2017-08-15 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the conference on Lie Algebras, Vertex Operator Algebras, and Related Topics, celebrating the 70th birthday of James Lepowsky and Robert Wilson, held from August 14–18, 2015, at the University of Notre Dame, Notre Dame, Indiana. Since their seminal work in the 1970s, Lepowsky and Wilson, their collaborators, their students, and those inspired by their work, have developed an amazing body of work intertwining the fields of Lie algebras, vertex algebras, number theory, theoretical physics, quantum groups, the representation theory of finite simple groups, and more. The papers presented here include recent results and descriptions of ongoing research initiatives representing the broad influence and deep connections brought about by the work of Lepowsky and Wilson and include a contribution by Yi-Zhi Huang summarizing some major open problems in these areas, in particular as they pertain to two-dimensional conformal field theory.

Author : James Lepowsky
Publisher : Springer Science & Business Media
ISBN 13 : 0817681868
Total Pages : 330 pages
Book Rating : 4.69/5 ( download)

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Download or read book Introduction to Vertex Operator Algebras and Their Representations written by James Lepowsky and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: * 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.

Author : Edward Frenkel
Publisher : American Mathematical Soc.
ISBN 13 : 0821836749
Total Pages : 418 pages
Book Rating : 4.43/5 ( download)

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Download or read book Vertex Algebras and Algebraic Curves written by Edward Frenkel and published by American Mathematical Soc.. This book was released on 2004-08-25 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vertex algebras are algebraic objects that encapsulate the concept of operator product expansion from two-dimensional conformal field theory. Vertex algebras are fast becoming ubiquitous in many areas of modern mathematics, with applications to representation theory, algebraic geometry, the theory of finite groups, modular functions, topology, integrable systems, and combinatorics. This book is an introduction to the theory of vertex algebras with a particular emphasis on the relationship with the geometry of algebraic curves. The notion of a vertex algebra is introduced in a coordinate-independent way, so that vertex operators become well defined on arbitrary smooth algebraic curves, possibly equipped with additional data, such as a vector bundle. Vertex algebras then appear as the algebraic objects encoding the geometric structure of various moduli spaces associated with algebraic curves. Therefore they may be used to give a geometric interpretation of various questions of representation theory. The book contains many original results, introduces important new concepts, and brings new insights into the theory of vertex algebras. The authors have made a great effort to make the book self-contained and accessible to readers of all backgrounds. Reviewers of the first edition anticipated that it would have a long-lasting influence on this exciting field of mathematics and would be very useful for graduate students and researchers interested in the subject. This second edition, substantially improved and expanded, includes several new topics, in particular an introduction to the Beilinson-Drinfeld theory of factorization algebras and the geometric Langlands correspondence.

Author : Yi-Zhi Huang
Publisher : American Mathematical Soc.
ISBN 13 : 0821839861
Total Pages : 500 pages
Book Rating : 4.67/5 ( download)

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Download or read book Lie Algebras, Vertex Operator Algebras and Their Applications written by Yi-Zhi Huang and published by American Mathematical Soc.. This book was released on 2007 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles in this book are based on talks given at the international conference 'Lie algebras, vertex operator algebras and their applications'. The focus of the papers is mainly on Lie algebras, quantum groups, vertex operator algebras and their applications to number theory, combinatorics and conformal field theory.

Author : M. J. Bergvelt
Publisher : American Mathematical Soc.
ISBN 13 : 0821848402
Total Pages : 246 pages
Book Rating : 4.01/5 ( download)

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Download or read book Vertex Operator Algebras and Related Areas written by M. J. Bergvelt and published by American Mathematical Soc.. This book was released on 2009-10-01 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vertex operator algebras were introduced to mathematics in the work of Richard Borcherds, Igor Frenkel, James Lepowsky and Arne Meurman as a mathematically rigorous formulation of chiral algebras of two-dimensional conformal field theory. The aim was to use vertex operator algebras to explain and prove the remarkable Monstrous Moonshine conjectures in group theory. The theory of vertex operator algebras has now grown into a major research area in mathematics. These proceedings contain expository lectures and research papers presented during the international conference on Vertex Operator Algebras and Related Areas, held at Illinois State University in Normal, IL, from July 7 to July 11, 2008. The main aspects of this conference were connections and interactions of vertex operator algebras with the following areas: conformal field theories, quantum field theories, Hopf algebra, infinite dimensional Lie algebras, and modular forms. This book will be useful for researchers as well as for graduate students in mathematics and physics. Its purpose is not only to give an up-to-date overview of the fields covered by the conference but also to stimulate new directions and discoveries by experts in the areas.

Author : Chongying Dong
Publisher : Springer Science & Business Media
ISBN 13 : 1461203538
Total Pages : 207 pages
Book Rating : 4.37/5 ( download)

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Download or read book Generalized Vertex Algebras and Relative Vertex Operators written by Chongying Dong and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: The rapidly-evolving theory of vertex operator algebras provides deep insight into many important algebraic structures. Vertex operator algebras can be viewed as "complex analogues" of both Lie algebras and associative algebras. The monograph is written in a n accessible and self-contained manner, with detailed proofs and with many examples interwoven through the axiomatic treatment as motivation and applications. It will be useful for research mathematicians and theoretical physicists working the such fields as representation theory and algebraic structure sand will provide the basis for a number of graduate courses and seminars on these and related topics.

Author : Neelacanta Sthanumoorthy
Publisher : American Mathematical Soc.
ISBN 13 : 0821833375
Total Pages : 384 pages
Book Rating : 4.77/5 ( download)

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Download or read book Kac-Moody Lie Algebras and Related Topics written by Neelacanta Sthanumoorthy and published by American Mathematical Soc.. This book was released on 2004 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Kailash C. Misra
Publisher : American Mathematical Soc.
ISBN 13 : 1470418444
Total Pages : 355 pages
Book Rating : 4.41/5 ( download)

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Download or read book Lie Algebras, Lie Superalgebras, Vertex Algebras and Related Topics written by Kailash C. Misra and published by American Mathematical Soc.. This book was released on 2016-06-28 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Matthew Krauel
Publisher : American Mathematical Soc.
ISBN 13 : 1470449382
Total Pages : 250 pages
Book Rating : 4.84/5 ( download)

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Download or read book Vertex Operator Algebras, Number Theory and Related Topics written by Matthew Krauel and published by American Mathematical Soc.. This book was released on 2020-07-13 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the International Conference on Vertex Operator Algebras, Number Theory, and Related Topics, held from June 11–15, 2018, at California State University, Sacramento, California. The mathematics of vertex operator algebras, vector-valued modular forms and finite group theory continues to provide a rich and vibrant landscape in mathematics and physics. The resurgence of moonshine related to the Mathieu group and other groups, the increasing role of algebraic geometry and the development of irrational vertex operator algebras are just a few of the exciting and active areas at present. The proceedings center around active research on vertex operator algebras and vector-valued modular forms and offer original contributions to the areas of vertex algebras and number theory, surveys on some of the most important topics relevant to these fields, introductions to new fields related to these and open problems from some of the leaders in these areas.

Author : Stephen Berman
Publisher : American Mathematical Soc.
ISBN 13 : 0821828568
Total Pages : 265 pages
Book Rating : 4.64/5 ( download)

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Download or read book Vertex Operator Algebras in Mathematics and Physics written by Stephen Berman and published by American Mathematical Soc.. This book was released on 2003 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vertex operator algebras are a class of algebras underlying a number of recent constructions, results, and themes in mathematics. These algebras can be understood as ''string-theoretic analogues'' of Lie algebras and of commutative associative algebras. They play fundamental roles in some of the most active research areas in mathematics and physics. Much recent progress in both physics and mathematics has benefited from cross-pollination between the physical and mathematical points of view. This book presents the proceedings from the workshop, ''Vertex Operator Algebras in Mathematics and Physics'', held at The Fields Institute. It consists of papers based on many of the talks given at the conference by leading experts in the algebraic, geometric, and physical aspects of vertex operator algebra theory. The book is suitable for graduate students and research mathematicians interested in the major themes and important developments on the frontier of research in vertex operator algebra theory and its applications in mathematics and physics.