Vertex Operator Algebras and the Monster

Author: Igor Frenkel,James Lepowsky,Arne Meurman

Publisher: Academic Press

ISBN: 9780080874548

Category: Mathematics

Page: 508

View: 1380

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."
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Vertex Operator Algebras and Related Areas

An International Conference in Honor of Geoffrey Mason's 60th Birthday : July 7-11, 2008, Illinois State University, Normal, Illinois

Author: M. J. Bergvelt,Gaywalee Yamskulna,Wenhua Zhao

Publisher: American Mathematical Soc.

ISBN: 0821848402

Category: Mathematics

Page: 225

View: 2364

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.
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Vertex Operator Algebras in Mathematics and Physics

Author: Stephen Berman

Publisher: American Mathematical Soc.

ISBN: 9780821871447

Category: Mathematics

Page: 249

View: 5760

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.
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Lie Algebras, Vertex Operator Algebras, and Related Topics

Author: Katrina Barron,Elizabeth Jurisich,Antun Milas,Kailash Misr

Publisher: American Mathematical Soc.

ISBN: 1470426668

Category: Lie algebras

Page: 274

View: 8358

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.
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Lie Algebras, Vertex Operator Algebras and Their Applications

International Conference in Honor of James Lepowsky and Robert Wilson on Their Sixtieth Birthdays, May 17-21, 2005, North Carolina State University, Raleigh, North Carolina

Author: James Lepowsky,Robert L. Wilson,Yi-Zhi Huang,Kailash C. Misra

Publisher: American Mathematical Soc.

ISBN: 0821839861

Category: Mathematics

Page: 474

View: 6325

The articles in this book are based on talks given at the international conference ""Lie algebras, vertex operator algebras and their applications"", in honor of James Lepowsky and Robert Wilson on their sixtieth birthdays, held in May of 2005 at North Carolina State University. Some of the papers in this volume give inspiring expositions on the development and status of their respective research areas. Others outline and explore the challenges as well as the future directions of research for the twenty-first century. The focus of the papers in this volume is mainly on Lie algebras, quantum groups, vertex operator algebras and their applications to number theory, combinatorics and conformal field theory. This book is useful for graduate students and researchers in mathematics and mathematical physics who want to be introduced to different areas of current research or explore the frontiers of research in the areas mentioned above.
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Introduction to Vertex Operator Algebras and Their Representations

Author: James Lepowsky,Haisheng Li

Publisher: Springer Science & Business Media

ISBN: 9780817634087

Category: Mathematics

Page: 318

View: 8404

The deep and relatively new field of vertex operator algebras is intimately related to a variety of areas in mathematics and physics: for example, the concepts of "monstrous moonshine," infinite-dimensional Lie theory, string theory, and conformal field theory. This book introduces the reader to the fundamental theory of vertex operator algebras and its basic techniques and examples. Beginning with a detailed presentation of the theoretical foundations and proceeding to a range of applications, the text includes a number of new, original results and also highlights and brings fresh perspective to important works of many researchers. After introducing the elementary "formal calculus'' underlying the subject, the book provides an axiomatic development of vertex operator algebras and their modules, expanding on the early contributions of R. Borcherds, I. Frenkel, J. Lepowsky, A. Meurman, Y.-Z. Huang, C. Dong, Y. Zhu and others. The concept of a "representation'' of a vertex (operator) algebra is treated in detail, following and extending the work of H. Li; this approach is used to construct important families of vertex (operator) algebras and their modules. Requiring only a familiarity with basic algebra, Introduction to Vertex Operator Algebras and Their Representations will be useful for graduate students and researchers in mathematics and physics. The booka??s presentation of the core topics will equip readers to embark on many active research directions related to vertex operator algebras, group theory, representation theory, and string theory.
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Sūgaku Expositions

A Translation of Sūgaku

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 5306

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Groups and Combinatorics―in memory of Michio Suzuki

Author: Eiichi Bannai

Publisher: Amer Mathematical Society

ISBN: N.A

Category: Mathematics

Page: 474

View: 8429

In honor of Professor Michio Suzuki's 70th birthday, a conference was held at the International Christian University (Tokyo, Japan). This book presents the proceedings of that conference. Professor Suzuki had a profound influence on the development of group theory over the last 50 years. It's generally believed that his work in the 1950s ignited work on the classification of finite simple groups, and in the 1960s and 1970s, he was a leader in its development. Just prior to his death in 1998, Professor Suzuki completed a 150-page manuscript containing his most recent contribution to group theory. This paper, ``On the Prime Graph of a Finite Simple Group--an Application of the Method of Feit-Thompson-Bender-Glauberman'', is included in this volume. Here, the editors have been meticulous in making minimal corrections to the work in order to honor the writing style and original flow of Professor Suzuki's thoughts. The book also includes contributions from the speakers at the conference, as well as papers from researchers who shared close ties with Professor Suzuki.
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Functional Analysis

Author: Interuniverzitetski centar za postdiplomski studij (Dubrovnik, Croatia). Conference

Publisher: N.A

ISBN: N.A

Category: Functional analysis

Page: N.A

View: 4673

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Kac-Moody Groups, their Flag Varieties and Representation Theory

Author: Shrawan Kumar

Publisher: Springer Science & Business Media

ISBN: 9780817642273

Category: Mathematics

Page: 606

View: 4248

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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Taniguchi Conference on Mathematics Nara '98

Author: Masaki Maruyama,Toshikazu Sunada

Publisher: Amer Mathematical Society

ISBN: 9784931469136

Category: Mathematics

Page: 286

View: 9762

In 1974, Mr Taniguchi promoted and sponsored an International Symposium in various fields of science on a smaller scale. This volume is a collection of the research manuscripts written by the invited speakers at the final conference set up by the Taniguchi Foundation, the Taniguchi Conference on Mathematics 1998, held in Nara, Japan.
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PAMQ

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 8706

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