Elliptic Genera And Vertex Operator Super Algebras
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Elliptic Genera and Vertex Operator Super Algebras
Author | : Hirotaka Tamanoi |
Publsiher | : Springer |
Total Pages | : 397 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 9783540487883 |
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This monograph deals with two aspects of the theory of elliptic genus: its topological aspect involving elliptic functions, and its representation theoretic aspect involving vertex operator super-algebras. For the second aspect, elliptic genera are shown to have the structure of modules over certain vertex operator super-algebras. The vertex operators corresponding to parallel tensor fields on closed Riemannian Spin Kähler manifolds such as Riemannian tensors and Kähler forms are shown to give rise to Virasoro algebras and affine Lie algebras. This monograph is chiefly intended for topologists and it includes accounts on topics outside of topology such as vertex operator algebras.
Introduction to Vertex Operator Superalgebras and Their Modules
Author | : Xiaoping Xu |
Publsiher | : Springer Science & Business Media |
Total Pages | : 380 |
Release | : 1998-09-30 |
Genre | : Mathematics |
ISBN | : 0792352424 |
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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.
Generalized Vertex Algebras and Relative Vertex Operators
Author | : Chongying Dong,James Lepowsky |
Publsiher | : Springer Science & Business Media |
Total Pages | : 207 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9781461203537 |
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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
Author | : James Lepowsky,Haisheng Li |
Publsiher | : Springer Science & Business Media |
Total Pages | : 330 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9780817681869 |
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* 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.
Proceedings of the Japan Academy
Author | : Nihon Gakushiin |
Publsiher | : Unknown |
Total Pages | : 324 |
Release | : 1995 |
Genre | : Mathematics |
ISBN | : UOM:39015035205171 |
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Transseries and Real Differential Algebra
Author | : Joris van der Hoeven |
Publsiher | : Springer |
Total Pages | : 265 |
Release | : 2006-10-31 |
Genre | : Mathematics |
ISBN | : 9783540355915 |
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Transseries are formal objects constructed from an infinitely large variable x and the reals using infinite summation, exponentiation and logarithm. They are suitable for modeling "strongly monotonic" or "tame" asymptotic solutions to differential equations and find their origin in at least three different areas of mathematics: analysis, model theory and computer algebra. They play a crucial role in Écalle's proof of Dulac's conjecture, which is closely related to Hilbert's 16th problem. The aim of the present book is to give a detailed and self-contained exposition of the theory of transseries, in the hope of making it more accessible to non-specialists.
Spinor Construction of Vertex Operator Algebras Triality and E8 1
Author | : Alex J. Feingold,Igor Frenkel,John F. X. Ries |
Publsiher | : American Mathematical Soc. |
Total Pages | : 146 |
Release | : 1991 |
Genre | : Mathematics |
ISBN | : 9780821851289 |
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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 Their Applications
Author | : Yi-Zhi Huang,Kailash C. Misra |
Publsiher | : American Mathematical Soc. |
Total Pages | : 500 |
Release | : 2007 |
Genre | : Mathematics |
ISBN | : 9780821839867 |
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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.