Generalized Vertex Algebras And Relative Vertex Operators

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Generalized Vertex Algebras And Relative Vertex Operators

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Author : Chongying Dong
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Generalized Vertex Algebras And Relative Vertex Operators written by Chongying Dong and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

In the past few years, vertex operator algebra theory has been growing both in intrinsic interest and in the scope of its interconnections with areas of mathematics and physics. The structure and representation theory of vertex operator algebras is deeply related to such subjects as monstrous moonshine, conformal field theory and braid group theory. Vertex operator algebras are the mathematical counterpart of chiral algebras in conformal field theory. In the Introduction which follows, we sketch some of the main themes in the historical development and mathematical and physical motivations of these ideas, and some of the current issues. Given a vertex operator algebra, it is important to consider not only its modules (representations) but also intertwining operators among the mod ules. Matrix coefficients of compositions of these operators, corresponding to certain kinds of correlation functions in conformal field theory, lead natu rally to braid group representations. In the specialbut important case when these braid group representations are one-dimensional, one can combine the modules and intertwining operators with the algebra to form a structure satisfying axioms fairly close to those for a vertex operator algebra. These are the structures which form the main theme of this monograph. Another treatment of similar structures has been given by Feingold, Frenkel and Ries (see the reference [FFR] in the Bibliography), and in fact the material de veloped in the present work has close connections with much work of other people, as we explain in the Introduction and throughout the text.

Vertex Operator Algebras In Mathematics And Physics

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Author : Stephen Berman
language : en
Publisher: American Mathematical Soc.
Release Date :

Vertex Operator Algebras In Mathematics And Physics written by Stephen Berman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.

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.

Introduction To Vertex Operator Algebras And Their Representations

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Author : James Lepowsky
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Introduction To Vertex Operator Algebras And Their Representations written by James Lepowsky and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

* 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.

Introduction To Vertex Operator Superalgebras And Their Modules

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Author : Xiaoping Xu
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Introduction To Vertex Operator Superalgebras And Their Modules written by Xiaoping Xu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.

This book presents a systematic study on the structures of vertex operator superalgebras and their modules. Related theories of self-dual codes and lattices are included, as well as recent achievements on classifications of certain simple vertex operator superalgebras and their irreducible twisted modules, constructions of simple vertex operator superalgebras from graded associative algebras and their anti-involutions, self-dual codes and lattices. Audience: This book is of interest to researchers and graduate students in mathematics and mathematical physics.

Vertex Operator Algebras And Related Areas

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Author : M. J. Bergvelt
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-10-01

Vertex Operator Algebras And Related Areas written by M. J. Bergvelt and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-01 with Mathematics categories.

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.

Lie Algebras Vertex Operator Algebras And Their Applications

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Author : Yi-Zhi Huang
language : en
Publisher: American Mathematical Soc.
Release Date : 2007

Lie Algebras Vertex Operator Algebras And Their Applications written by Yi-Zhi Huang and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

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.

Vertex Algebras And Algebraic Curves

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Author : Edward Frenkel
language : en
Publisher: American Mathematical Soc.
Release Date : 2004-08-25

Vertex Algebras And Algebraic Curves written by Edward Frenkel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-08-25 with Mathematics categories.

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.

Lie Algebras Vertex Operator Algebras And Related Topics

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Author : Katrina Barron
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-08-15

Lie Algebras Vertex Operator Algebras And Related Topics written by Katrina Barron and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-15 with Mathematics categories.

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.

Extensions Of The Jacobi Identity For Vertex Operators And Standard A 1 1 Modules

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Author : Cristiano Husu
language : en
Publisher: American Mathematical Soc.
Release Date : 1993

Extensions Of The Jacobi Identity For Vertex Operators And Standard A 1 1 Modules written by Cristiano Husu and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.

The main axiom for a vertex operator algebra (over a field of characteristic zero), the Jacobi identity, is extended to multi-operator identities. Then relative [bold capital]Z2-twisted vertex operators are introduced and a Jacobi identity for these operators is established. Then these ideas are used to interpret and recover the twisted [bold capital]Z-operators and corresponding generating function identities developed by Lepowsky and R. L. Wilson. This work is closely related to the twisted parafermion algebra constructed by Zamolodchikov-Fateev.

Bosonic Construction Of Vertex Operator Para Algebras From Symplectic Affine Kac Moody Algebras

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Author : Michael David Weiner
language : en
Publisher: American Mathematical Soc.
Release Date : 1998

Bosonic Construction Of Vertex Operator Para Algebras From Symplectic Affine Kac Moody Algebras written by Michael David Weiner and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.

Begins with the bosonic construction of four level -1/2 irreducible representations of the symplectic affine Kac-Moody Lie algebra Cl. The direct sum of two of these is given the structure of a vertex operator algebra (VOA), and the direct sum of the other two is given the structure of a twisted VOA-module. The dissertation includes the bosonic analog of the fermionic construction of a vertex operator superalgebra from the four level 1 irreducible modules of type Dl. No index. Annotation copyrighted by Book News, Inc., Portland, OR