Read Books Online and Download eBooks, EPub, PDF, Mobi, Kindle, Text Full Free.
Vertex Operator Algebras And The Monster
Download Vertex Operator Algebras And The Monster full books in PDF, epub, and Kindle. Read online Vertex Operator Algebras And The Monster ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Book Synopsis Vertex Operator Algebras and the Monster by : Igor Frenkel
Download or read book Vertex Operator Algebras and the Monster written by Igor Frenkel and published by Academic Press. This book was released on 1989-05-01 with total page 563 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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."
Book Synopsis Spinor Construction of Vertex Operator Algebras, Triality, and E8(1) by : Alex J. Feingold
Download or read book Spinor Construction of Vertex Operator Algebras, Triality, and E8(1) written by Alex J. Feingold and published by American Mathematical Soc.. This book was released on 1991 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of vertex operator algebras is a remarkably rich new mathematical field which captures the algebraic content of conformal field theory in physics. Ideas leading up to this theory appeared in physics as part of statistical mechanics and string theory. In mathematics, the axiomatic definitions crystallized in the work of Borcherds and in Vertex Operator Algebras and the Monster, by Frenkel, Lepowsky, and Meurman. The structure of monodromies of intertwining operators for modules of vertex operator algebras yields braid group representations and leads to natural generalizations of vertex operator algebras, such as superalgebras and para-algebras. Many examples of vertex operator algebras and their generalizations are related to constructions in classical representation theory and shed new light on the classical theory. This book accomplishes several goals. The authors provide an explicit spinor construction, using only Clifford algebras, of a vertex operator superalgebra structure on the direct sum of the basic and vector modules for the affine Kac-Moody algebra $D^{(1)}_n$. They also review and extend Chevalley's spinor construction of the 24-dimensional commutative nonassociative algebraic structure and triality on the direct sum of the three 8-dimensional $D_4$-modules. Vertex operator para-algebras, introduced and developed independently in this book and by Dong and Lepowsky, are related to one-dimensional representations of the braid group. The authors also provide a unified approach to the Chevalley, Griess, and $E_8$ algebras and explain some of their similarities. A third goal is to provide a purely spinor construction of the exceptional affine Lie algebra $E^{(1)}_8$, a natural continuation of previous work on spinor and oscillator constructions of the classical affine Lie algebras. These constructions should easily extend to include the rest of the exceptional affine Lie algebras. The final objective is to develop an inductive technique of construction which could be applied to the Monster vertex operator algebra. Directed at mathematicians and physicists, this book should be accessible to graduate students with some background in finite-dimensional Lie algebras and their representations. Although some experience with affine Kac-Moody algebras would be useful, a summary of the relevant parts of that theory is included. This book shows how the concepts and techniques of Lie theory can be generalized to yield the algebraic structures associated with conformal field theory. The careful reader will also gain a detailed knowledge of how the spinor construction of classical triality lifts to the affine algebras and plays an important role in a spinor construction of vertex operator algebras, modules, and intertwining operators with nontrivial monodromies.
Book Synopsis Vertex Algebras and Algebraic Curves by : Edward Frenkel
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.
Book Synopsis Introduction to Vertex Operator Algebras and Their Representations by : James Lepowsky
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.
Book Synopsis On Axiomatic Approaches to Vertex Operator Algebras and Modules by : Igor Frenkel
Download or read book On Axiomatic Approaches to Vertex Operator Algebras and Modules written by Igor Frenkel and published by American Mathematical Soc.. This book was released on 1993 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt: The notion of vertex operator algebra arises naturally in the vertex operator construction of the Monster - the largest sporadic finite simple group. From another perspective, the theory of vertex operator algebras and their modules forms the algebraic foundation of conformal field theory. Vertex operator algebras and conformal field theory are now known to be deeply related to many important areas of mathematics. This essentially self-contained monograph develops the basic axiomatic theory of vertex operator algebras and their modules and intertwining operators, following a fundamental analogy with Lie algebra theory. The main axiom, the 'Jacobi(-Cauchy) identity', is a far-reaching analog of the Jacobi identity for Lie algebras.The authors show that the Jacobi identity is equivalent to suitably formulated rationality, commutativity, and associativity properties of products of quantum fields. A number of other foundational and useful results are also developed. This work was originally distributed as a preprint in 1989, and in view of the current widespread interest in the subject among mathematicians and theoretical physicists, its publication and availability should prove no less useful than when it was written.
Book Synopsis Moonshine beyond the Monster by : Terry Gannon
Download or read book Moonshine beyond the Monster written by Terry Gannon and published by Cambridge University Press. This book was released on 2023-07-31 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Vertex Algebras for Beginners by : Victor G. Kac
Download or read book Vertex Algebras for Beginners written by Victor G. Kac and published by American Mathematical Soc.. This book was released on 1998 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on courses given by the author at MIT and at Rome University in spring 1997, this book presents an introduction to algebraic aspects of conformal field theory. It includes material on the foundations of a rapidly growing area of algebraic conformal theory.
Book Synopsis From Vertex Operator Algebras to Conformal Nets and Back by : Sebastiano Carpi
Download or read book From Vertex Operator Algebras to Conformal Nets and Back written by Sebastiano Carpi and published by American Mathematical Soc.. This book was released on 2018-08-09 with total page 85 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider unitary simple vertex operator algebras whose vertex operators satisfy certain energy bounds and a strong form of locality and call them strongly local. They present a general procedure which associates to every strongly local vertex operator algebra V a conformal net AV acting on the Hilbert space completion of V and prove that the isomorphism class of AV does not depend on the choice of the scalar product on V. They show that the class of strongly local vertex operator algebras is closed under taking tensor products and unitary subalgebras and that, for every strongly local vertex operator algebra V, the map W↦AW gives a one-to-one correspondence between the unitary subalgebras W of V and the covariant subnets of AV.
Book Synopsis Topological Field Theory, Primitive Forms and Related Topics by : A. Kashiwara
Download or read book Topological Field Theory, Primitive Forms and Related Topics written by A. Kashiwara and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: As the interaction of mathematics and theoretical physics continues to intensify, the theories developed in mathematics are being applied to physics, and conversely. This book centers around the theory of primitive forms which currently plays an active and key role in topological field theory (theoretical physics), but was originally developed as a mathematical notion to define a "good period mapping" for a family of analytic structures. The invited papers in this volume are expository in nature by participants of the Taniguchi Symposium on "Topological Field Theory, Primitive Forms and Related Topics" and the RIMS Symposium bearing the same title, both held in Kyoto. The papers reflect the broad research of some of the world's leading mathematical physicists, and should serve as an excellent resource for researchers as well as graduate students of both disciplines.
Book Synopsis Vertex Operators in Mathematics and Physics by : J. Lepowsky
Download or read book Vertex Operators in Mathematics and Physics written by J. Lepowsky and published by Springer Science & Business Media. This book was released on 2013-03-08 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Lie Algebras, Vertex Operator Algebras and Their Applications by : Yi-Zhi Huang
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.
Book Synopsis Vertex Operator Algebras and Related Areas by : M. J. Bergvelt
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.
Book Synopsis Vertex Operator Algebras in Mathematics and Physics by : Stephen Berman
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.
Book Synopsis The Monster and Lie Algebras by : Joseph Ferrar
Download or read book The Monster and Lie Algebras written by Joseph Ferrar and published by Walter de Gruyter. This book was released on 2011-06-24 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thisseries is devoted to the publication of monographs, lecture resp. seminar notes, and other materials arising from programs of the OSU Mathemaical Research Institute. This includes proceedings of conferences or workshops held at the Institute, and other mathematical writings.
Book Synopsis Vertex Operator Algebras in Mathematics and Physics by : Stephen Berman
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 with total page 268 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.
Book Synopsis Kac-Moody and Virasoro Algebras by : Peter Goddard
Download or read book Kac-Moody and Virasoro Algebras written by Peter Goddard and published by World Scientific. This book was released on 1988 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume reviews the subject of Kac-Moody and Virasoro Algebras. It serves as a reference book for physicists with commentary notes and reprints.
Book Synopsis Vertex Operator Algebras, Number Theory and Related Topics by : Matthew Krauel
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.
