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lgli/M_Mathematics/Msb_Sborniki/Mmams_Memoirs AMS/Frenkel I.B., Huang Y., Lepowsky J. On axiomatic approaches to vertex operator algebras and modules (MEMO0494, AMS, 1993)(ISBN 9780821825556)(600dpi)(T)(O)(79s).djvu
On Axiomatic Approaches To Vertex Operator Algebras And Modules (memoirs Of The American Mathematica 🔍
Igor B. Frenkel, Yi-Zhi Huang, James Lepowsky American Mathematical Society, Memoirs of the American Mathematical Society,, no. 494, Providence, R.I, Rhode Island, 1993
English [en] · DJVU · 0.7MB · 1993 · 📘 Book (non-fiction) · 🚀/lgli/lgrs/nexusstc/zlib · Save
description
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.
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nexusstc/On Axiomatic Approaches to Vertex Operator Algebras and Modules/de3eb93805d90954c960fdffbdfc23b2.djvu
Alternative filename
lgli/Frenkel_I.B.__Huang_Y.__Lepowsky_J._On_axiomatic_approaches_to_vertex_operator_algebras_and_modules_(MEMO0494__AMS__1993)(ISBN_9780821825556)(600dpi)(T)(O)(79s).djvu
Alternative filename
lgrsnf/Frenkel_I.B.__Huang_Y.__Lepowsky_J._On_axiomatic_approaches_to_vertex_operator_algebras_and_modules_(MEMO0494__AMS__1993)(ISBN_9780821825556)(600dpi)(T)(O)(79s).djvu
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zlib/Mathematics/Igor B. Frenkel, Yi-Zhi Huang, James Lepowsky/On Axiomatic Approaches to Vertex Operator Algebras and Modules_3348992.djvu
Alternative title
Memoirs of the American Mathematical Society
Alternative author
Frenkel, Igor; Lepowsky, J.; Huang, Yi-Zhi
Alternative author
Frenkel, Igor B., Huang, Yi-zhi, Lepowsk
Alternative edition
United States, United States of America
metadata comments
0
metadata comments
lg2107156
metadata comments
{"isbns":["0821825550","9780821825556"],"last_page":64,"publisher":"Amer Mathematical Society","series":"Memoirs AMS 494"}
metadata comments
Includes bibliographical references (p. 64).
"July 1993, vol. 104, no. 494 (first of 6 numbers)."
Alternative description
The basic definitions and properties of vertex operator algebras, modules, intertwining operators and related concepts are presented, following a fundamental analogy with Lie algebra theory. The first steps in the development of the general theory are taken, and various natural and useful reformulations of the axioms are given. In particular, tensor products of algebras and modules, adjoint vertex operators and contragradient modules, adjoint intertwining operators and fusion rules are studied in greater depth. This paper lays the monodromy-free axiomatic foundation of the general theory of vertex operator algebras, modules and intertwining operators
date open sourced
2017-09-11
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