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Author | : J. Lepowsky |
Publisher | : Springer Science & Business Media |
Total Pages | : 484 |
Release | : 2013-03-08 |
Genre | : Science |
ISBN | : 146139550X |
Download Vertex Operators in Mathematics and Physics Book in PDF, ePub and Kindle
James Lepowsky t The search for symmetry in nature has for a long time provided representation theory with perhaps its chief motivation. According to the standard approach of Lie theory, one looks for infinitesimal symmetry -- Lie algebras of operators or concrete realizations of abstract Lie algebras. A central theme in this volume is the construction of affine Lie algebras using formal differential operators called vertex operators, which originally appeared in the dual-string theory. Since the precise description of vertex operators, in both mathematical and physical settings, requires a fair amount of notation, we do not attempt it in this introduction. Instead we refer the reader to the papers of Mandelstam, Goddard-Olive, Lepowsky-Wilson and Frenkel-Lepowsky-Meurman. We have tried to maintain consistency of terminology and to some extent notation in the articles herein. To help the reader we shall review some of the terminology. We also thought it might be useful to supplement an earlier fairly detailed exposition of ours [37] with a brief historical account of vertex operators in mathematics and their connection with affine algebras. Since we were involved in the development of the subject, the reader should be advised that what follows reflects our own understanding. For another view, see [29].1 t Partially supported by the National Science Foundation through the Mathematical Sciences Research Institute and NSF Grant MCS 83-01664. 1 We would like to thank Igor Frenkel for his valuable comments on the first draft of this introduction.
Author | : Igor Frenkel |
Publisher | : Academic Press |
Total Pages | : 563 |
Release | : 1989-05-01 |
Genre | : Mathematics |
ISBN | : 0080874541 |
Download Vertex Operator Algebras and the Monster Book in PDF, ePub and Kindle
This work is motivated by and develops connections between several branches of mathematics and physics--the theories of Lie algebras, finite groups and modular functions in mathematics, and string theory in physics. The first part of the book presents a new mathematical theory of vertex operator algebras, the algebraic counterpart of two-dimensional holomorphic conformal quantum field theory. The remaining part constructs the Monster finite simple group as the automorphism group of a very special vertex operator algebra, called the "moonshine module" because of its relevance to "monstrous moonshine."
Author | : Stephen Berman |
Publisher | : American Mathematical Soc. |
Total Pages | : 265 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 0821828568 |
Download Vertex Operator Algebras in Mathematics and Physics Book in PDF, ePub and Kindle
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.
Author | : Stephen Berman |
Publisher | : American Mathematical Soc. |
Total Pages | : 268 |
Release | : |
Genre | : Mathematics |
ISBN | : 9780821871447 |
Download Vertex Operator Algebras in Mathematics and Physics Book in PDF, ePub and Kindle
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.
Author | : J. Lepowsky |
Publisher | : |
Total Pages | : 500 |
Release | : 2014-01-15 |
Genre | : |
ISBN | : 9781461395515 |
Download Vertex Operators in Mathematics and Physics Book in PDF, ePub and Kindle
Author | : James Lepowsky |
Publisher | : Springer Science & Business Media |
Total Pages | : 330 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 0817681868 |
Download Introduction to Vertex Operator Algebras and Their Representations Book in PDF, ePub and Kindle
* 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 | : J. Lepowsky |
Publisher | : Springer |
Total Pages | : 482 |
Release | : 1985-01-15 |
Genre | : Science |
ISBN | : 9780387961217 |
Download Vertex Operators in Mathematics and Physics Book in PDF, ePub and Kindle
James Lepowsky t The search for symmetry in nature has for a long time provided representation theory with perhaps its chief motivation. According to the standard approach of Lie theory, one looks for infinitesimal symmetry -- Lie algebras of operators or concrete realizations of abstract Lie algebras. A central theme in this volume is the construction of affine Lie algebras using formal differential operators called vertex operators, which originally appeared in the dual-string theory. Since the precise description of vertex operators, in both mathematical and physical settings, requires a fair amount of notation, we do not attempt it in this introduction. Instead we refer the reader to the papers of Mandelstam, Goddard-Olive, Lepowsky-Wilson and Frenkel-Lepowsky-Meurman. We have tried to maintain consistency of terminology and to some extent notation in the articles herein. To help the reader we shall review some of the terminology. We also thought it might be useful to supplement an earlier fairly detailed exposition of ours [37] with a brief historical account of vertex operators in mathematics and their connection with affine algebras. Since we were involved in the development of the subject, the reader should be advised that what follows reflects our own understanding. For another view, see [29].1 t Partially supported by the National Science Foundation through the Mathematical Sciences Research Institute and NSF Grant MCS 83-01664. 1 We would like to thank Igor Frenkel for his valuable comments on the first draft of this introduction.
Author | : Edward Frenkel |
Publisher | : American Mathematical Soc. |
Total Pages | : 418 |
Release | : 2004-08-25 |
Genre | : Mathematics |
ISBN | : 0821836749 |
Download Vertex Algebras and Algebraic Curves Book in PDF, ePub and Kindle
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. |
Total Pages | : 500 |
Release | : 2007 |
Genre | : Mathematics |
ISBN | : 0821839861 |
Download Lie Algebras, Vertex Operator Algebras and Their Applications Book in PDF, ePub and Kindle
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 | : Stephen Berman |
Publisher | : |
Total Pages | : |
Release | : 2003 |
Genre | : Mathematical physics |
ISBN | : 9781470430733 |
Download Vertex operator algebras in mathematics and physics Book in PDF, ePub and Kindle
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.