Spinor Construction Of Vertex Operator Algebras Triality And E8 1
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Spinor Construction Of Vertex Operator Algebras Triality And E 1 8
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Author : Alex J. Feingold
language : en
Publisher: American Mathematical Soc.
Release Date : 1991
Spinor Construction Of Vertex Operator Algebras Triality And E 1 8 written by Alex J. Feingold 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 1991 with Mathematics categories.
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 yield 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 Dn(1). 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 D4-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, Greiss, and E8 algebras and explain some of their similarities. A Third goal is to provide a purely spinor construction of the exceptional affine Lie algebra E8(1), 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 the spinor construction of vertex operator algebras, modules, and intertwining operators with nontrivial monodromies.
Lie Theory And Its Applications In Physics
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Author : Vladimir Dobrev
language : en
Publisher: Springer
Release Date : 2015-01-26
Lie Theory And Its Applications In Physics written by Vladimir Dobrev and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-26 with Mathematics categories.
Traditionally, Lie theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrization of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry which is very helpful in understanding its structure. Geometrization and symmetries are meant in their widest sense, i.e., representation theory, algebraic geometry, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear PDE, special functions, and others. Furthermore, the necessary tools from functional analysis and number theory are included. This is a big interdisciplinary and interrelated field. Samples of these fresh trends are presented in this volume, based on contributions from the Workshop "Lie Theory and Its Applications in Physics" held near Varna (Bulgaria) in June 2013. This book is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists and researchers in the field of Lie Theory.
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.
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 Kac-Moody algebras 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
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.
On Axiomatic Approaches To Vertex Operator Algebras And Modules
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Author : Igor Frenkel
language : en
Publisher: American Mathematical Soc.
Release Date : 1993
On Axiomatic Approaches To Vertex Operator Algebras And Modules written by Igor 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 1993 with Mathematics categories.
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.
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.
Lie Algebras Vertex Operator Algebras And Their Applications
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Author : Yi-Zhi Huang
language : en
Publisher: American Mathematical Soc.
Release Date : 2007-10-04
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 2007-10-04 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'', 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.
Vertex Operator Algebras And Related Areas
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Author : M. J. Bergvelt
language : en
Publisher: American Mathematical Soc.
Release Date : 2009
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 with Hopf algebras categories.
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 : 1998-01-01
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 1998-01-01 with Mathematics categories.
Inspired by mathematical structures found by theoretical physicists and by the desire to understand the "monstrous moonshine" of the Monster group, Borcherds, Frenkel, Lepowsky, and Meurman introduced the definition of vertex operator algebra (VOA). An important