Generalized Vertex Algebras And Relative Vertex Operators

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Generalized Vertex Algebras and Relative Vertex Operators

Chongying Dong,James Lepowsky
Generalized Vertex Algebras and Relative Vertex Operators Book PDF

Author : Chongying Dong,James Lepowsky
Publisher : Springer Science & Business Media
Page : 207 pages
File Size : 51,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461203537

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Generalized Vertex Algebras and Relative Vertex Operators by Chongying Dong,James Lepowsky Pdf

The rapidly-evolving theory of vertex operator algebras provides deep insight into many important algebraic structures. Vertex operator algebras can be viewed as "complex analogues" of both Lie algebras and associative algebras. The monograph is written in a n accessible and self-contained manner, with detailed proofs and with many examples interwoven through the axiomatic treatment as motivation and applications. It will be useful for research mathematicians and theoretical physicists working the such fields as representation theory and algebraic structure sand will provide the basis for a number of graduate courses and seminars on these and related topics.

Introduction to Vertex Operator Algebras and Their Representations

James Lepowsky,Haisheng Li
Introduction to Vertex Operator Algebras and Their Representations Book PDF

Author : James Lepowsky,Haisheng Li
Publisher : Springer Science & Business Media
Page : 330 pages
File Size : 50,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9780817681869

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Introduction to Vertex Operator Algebras and Their Representations by James Lepowsky,Haisheng Li Pdf

* 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.

Vertex Operator Algebras in Mathematics and Physics

Stephen Berman
Vertex Operator Algebras in Mathematics and Physics Book PDF

Author : Stephen Berman
Publisher : American Mathematical Soc.
Page : 268 pages
File Size : 55,5 Mb
Release : 2024-06-28
Category : Mathematics
ISBN : 0821871447

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Vertex Operator Algebras in Mathematics and Physics by Stephen Berman Pdf

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.

Extensions of the Jacobi Identity for Vertex Operators, and Standard $A^{(1)}_1$-Modules

Cristiano Husu
Extensions of the Jacobi Identity for Vertex Operators and Standard A 1 1 Modules Book PDF

Author : Cristiano Husu
Publisher : American Mathematical Soc.
Page : 85 pages
File Size : 45,7 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821825716

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Extensions of the Jacobi Identity for Vertex Operators, and Standard $A^{(1)}_1$-Modules by Cristiano Husu Pdf

This book extends the Jacobi identity, the main axiom for a vertex operator algebra, to multi-operator identities. Based on constructions of Dong and Lepowsky, relative ${\mathbf Z}_2$-twisted vertex operators are then introduced, and a Jacobi identity for these operators is established. Husu uses these ideas to interpret and recover the twisted Z -operators and corresponding generating function identities developed by Lepowsky and Wilson for the construction of the standard $A^{(1)}_1$-modules. The point of view of the Jacobi identity also shows the equivalence between these twisted Z-operator algebras and the (twisted) parafermion algebras constructed by Zamolodchikov and Fadeev. The Lepowsky-Wilson generating function identities correspond to the identities involved in the construction of a basis for the space of C-disorder fields of such parafermion algebras.

Vertex Algebras and Geometry

Thomas Creutzig,Andrew R. Linshaw
Vertex Algebras and Geometry Book PDF

Author : Thomas Creutzig,Andrew R. Linshaw
Publisher : American Mathematical Soc.
Page : 168 pages
File Size : 49,9 Mb
Release : 2018-07-20
Category : Geometry, Algebraic
ISBN : 9781470437176

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Vertex Algebras and Geometry by Thomas Creutzig,Andrew R. Linshaw Pdf

This book contains the proceedings of the AMS Special Session on Vertex Algebras and Geometry, held from October 8–9, 2016, and the mini-conference on Vertex Algebras, held from October 10–11, 2016, in Denver, Colorado. The papers cover vertex algebras in connection with geometry and tensor categories, with topics in vertex rings, chiral algebroids, the Higgs branch conjecture, and applicability and use of vertex tensor categories.

Lie Algebras, Vertex Operator Algebras and Their Applications

Yi-Zhi Huang,Kailash C. Misra
Lie Algebras Vertex Operator Algebras and Their Applications Book PDF

Author : Yi-Zhi Huang,Kailash C. Misra
Publisher : American Mathematical Soc.
Page : 500 pages
File Size : 54,8 Mb
Release : 2007
Category : Lie algebras
ISBN : 9780821839867

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Lie Algebras, Vertex Operator Algebras and Their Applications by Yi-Zhi Huang,Kailash C. Misra Pdf

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.

Bosonic Construction of Vertex Operator Para-Algebras from Symplectic Affine Kac-Moody Algebras

Michael David Weiner
Bosonic Construction of Vertex Operator Para Algebras from Symplectic Affine Kac Moody Algebras Book PDF

Author : Michael David Weiner
Publisher : American Mathematical Soc.
Page : 121 pages
File Size : 47,7 Mb
Release : 1998
Category : Kac-Moody algebras
ISBN : 9780821808665

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Bosonic Construction of Vertex Operator Para-Algebras from Symplectic Affine Kac-Moody Algebras by Michael David Weiner Pdf

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

Shape, Smoothness, and Invariant Stratification of an Attracting Set for Delayed Monotone Positive Feedback

Tibor Krisztin,Hans-Otto Walther,Jianhong Wu
Shape Smoothness and Invariant Stratification of an Attracting Set for Delayed Monotone Positive Feedback Book PDF

Author : Tibor Krisztin,Hans-Otto Walther,Jianhong Wu
Publisher : American Mathematical Soc.
Page : 526 pages
File Size : 44,6 Mb
Release : 2024-06-28
Category : Mathematics
ISBN : 0821871692

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Shape, Smoothness, and Invariant Stratification of an Attracting Set for Delayed Monotone Positive Feedback by Tibor Krisztin,Hans-Otto Walther,Jianhong Wu Pdf

This book contains recent results about the global dynamics defined by a class of delay differential equations which model basic feedback mechanisms and arise in a variety of applications such as neural networks. The authors describe in detail the geometric structure of a fundamental invariant set, which in special cases is the global attractor, and the asymptotic behavior of solution curves on it. The approach makes use of advanced tools which in recent years have been developed for the investigation of infinite-dimensional dynamical systems: local invariant manifolds and inclination lemmas for noninvertible maps, Floquet theory for delay differential equations, a priori estimates controlling the growth and decay of solutions with prescribed oscillation frequency, a discrete Lyapunov functional counting zeros, methods to represent invariant sets as graphs, and Poincaré-Bendixson techniques for classes of delay differential systems. Several appendices provide the general results needed in the case study, so the presentation is self-contained. Some of the general results are not available elsewhere, specifically on smooth infinite-dimensional centre-stable manifolds for maps. Results in the appendices will be useful for future studies of more complicated attractors of delay and partial differential equations.

Introduction to Vertex Operator Superalgebras and Their Modules

Xiaoping Xu
Introduction to Vertex Operator Superalgebras and Their Modules Book PDF

Author : Xiaoping Xu
Publisher : Springer Science & Business Media
Page : 371 pages
File Size : 42,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401590976

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Introduction to Vertex Operator Superalgebras and Their Modules by Xiaoping Xu Pdf

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.

Spinor Construction of Vertex Operator Algebras, Triality, and E8(1)

Alex J. Feingold,Igor Frenkel,John F. X. Ries
Spinor Construction of Vertex Operator Algebras Triality and E8 1 Book PDF

Author : Alex J. Feingold,Igor Frenkel,John F. X. Ries
Publisher : American Mathematical Soc.
Page : 146 pages
File Size : 42,8 Mb
Release : 1991
Category : Mathematics
ISBN : 9780821851289

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Spinor Construction of Vertex Operator Algebras, Triality, and E8(1) by Alex J. Feingold,Igor Frenkel,John F. X. Ries Pdf

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.

Lie Algebras, Vertex Operator Algebras, and Related Topics

Katrina Barron,Elizabeth Jurisich,Antun Milas,Kailash Misr
Lie Algebras Vertex Operator Algebras and Related Topics Book PDF

Author : Katrina Barron,Elizabeth Jurisich,Antun Milas,Kailash Misr
Publisher : American Mathematical Soc.
Page : 274 pages
File Size : 41,7 Mb
Release : 2017-08-15
Category : Lie algebras
ISBN : 9781470426668

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Lie Algebras, Vertex Operator Algebras, and Related Topics by Katrina Barron,Elizabeth Jurisich,Antun Milas,Kailash Misr Pdf

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.

Tensor Categories for Vertex Operator Superalgebra Extensions

Thomas Creutzig,Shashank Kanade,Robert McRae
Tensor Categories for Vertex Operator Superalgebra Extensions Book PDF

Author : Thomas Creutzig,Shashank Kanade,Robert McRae
Publisher : American Mathematical Society
Page : 194 pages
File Size : 40,8 Mb
Release : 2024-04-17
Category : Mathematics
ISBN : 9781470467241

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Tensor Categories for Vertex Operator Superalgebra Extensions by Thomas Creutzig,Shashank Kanade,Robert McRae Pdf

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Affine, Vertex and W-algebras

Dražen Adamović,Paolo Papi
Affine Vertex and W algebras Book PDF

Author : Dražen Adamović,Paolo Papi
Publisher : Springer Nature
Page : 218 pages
File Size : 55,7 Mb
Release : 2019-11-28
Category : Mathematics
ISBN : 9783030329068

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Affine, Vertex and W-algebras by Dražen Adamović,Paolo Papi Pdf

This book focuses on recent developments in the theory of vertex algebras, with particular emphasis on affine vertex algebras, affine W-algebras, and W-algebras appearing in physical theories such as logarithmic conformal field theory. It is widely accepted in the mathematical community that the best way to study the representation theory of affine Kac–Moody algebras is by investigating the representation theory of the associated affine vertex and W-algebras. In this volume, this general idea can be seen at work from several points of view. Most relevant state of the art topics are covered, including fusion, relationships with finite dimensional Lie theory, permutation orbifolds, higher Zhu algebras, connections with combinatorics, and mathematical physics. The volume is based on the INdAM Workshop Affine, Vertex and W-algebras, held in Rome from 11 to 15 December 2017. It will be of interest to all researchers in the field.

Lie Groups, Number Theory, and Vertex Algebras

Dražen Adamović,Andrej Dujella,Antun Milas,Pavle Pandžić
Lie Groups Number Theory and Vertex Algebras Book PDF

Author : Dražen Adamović,Andrej Dujella,Antun Milas,Pavle Pandžić
Publisher : American Mathematical Soc.
Page : 122 pages
File Size : 43,8 Mb
Release : 2021-05-10
Category : Education
ISBN : 9781470453510

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Lie Groups, Number Theory, and Vertex Algebras by Dražen Adamović,Andrej Dujella,Antun Milas,Pavle Pandžić Pdf

This volume contains the proceedings of the conference Representation Theory XVI, held from June 25–29, 2019, in Dubrovnik, Croatia. The articles in the volume address selected aspects of representation theory of reductive Lie groups and vertex algebras, and are written by prominent experts in the field as well as junior researchers. The three main topics of these articles are Lie theory, number theory, and vertex algebras.

Kac-Moody Lie Algebras and Related Topics

Neelacanta Sthanumoorthy,Kailash C. Misra
Kac Moody Lie Algebras and Related Topics Book PDF

Author : Neelacanta Sthanumoorthy,Kailash C. Misra
Publisher : American Mathematical Soc.
Page : 384 pages
File Size : 51,6 Mb
Release : 2004
Category : Kac-Moody algebras
ISBN : 9780821833377

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Kac-Moody Lie Algebras and Related Topics by Neelacanta Sthanumoorthy,Kailash C. Misra Pdf

This volume is the proceedings of the Ramanujan International Symposium on Kac-Moody Lie algebras and their applications. The symposium provided researchers in mathematics and physics with the opportunity to discuss new developments in this rapidly-growing area of research. The book contains several excellent articles with new and significant results. It is suitable for graduate students and researchers working in Kac-Moody Lie algebras, their applications, and related areas of research.