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Generalized Vertex Algebras and Relative Vertex Operators
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Catalogue Information
Field name
Details
Dewey Class
512
Title
Generalized Vertex Algebras and Relative Vertex Operators ([EBook] /) / by Chongying Dong, James Lepowsky.
Author
Dong, Chongying
Added Personal Name
Lepowsky, James
author.
Other name(s)
SpringerLink (Online service)
Publication
Boston, MA : : Birkhäuser Boston : : Imprint: Birkhäuser, , 1993.
Physical Details
IX, 206 p. : online resource.
Series
Progress in mathematics
0743-1643 ; ; 112
ISBN
9781461203537
Summary Note
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. They are mathematically precise counterparts of what are known in physics as chiral algebras, and in particular, they are intimately related to string theory and conformal field theory. Dong and Lepowsky have generalized the theory of vertex operator algebras in a systematic way at three successively more general levels, all of which incorporate one-dimensional braid groups representations intrinsically into the algebraic structure: First, the notion of "generalized vertex operator algebra" incorporates such structures as Z-algebras, parafermion algebras, and vertex operator superalgebras. Next, what they term "generalized vertex algebras" further encompass the algebras of vertex operators associated with rational lattices. Finally, the most general of the three notions, that of "abelian intertwining algebra," also illuminates the theory of intertwining operator for certain classes of vertex operator 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.:
Contents note
1 Introduction -- 2 The setting -- 3 Relative untwisted vertex operators -- 4 Quotient vertex operators -- 5 A Jacobi identity for relative untwisted vertex operators -- 6 Generalized vertex operator algebras and their modules -- 7 Duality for generalized vertex operator algebras -- 8 Monodromy representations of braid groups -- 9 Generalized vertex algebras and duality -- 10 Tensor products -- 11 Intertwining operators -- 12 Abelian intertwining algebras, third cohomology and duality -- 13 Affine Lie algebras and vertex operator algebras -- 14 Z-algebras and parafermion algebras -- List of frequently-used symbols, in order of appearance.
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site
http://dx.doi.org/10.1007/978-1-4612-0353-7
Links to Related Works
Subject References:
Algebra
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Associative rings
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Associative Rings and Algebras
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Group theory
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Group Theory and Generalizations
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Lie groups
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Mathematics
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Operator Theory
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Physics
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Rings (Algebra)
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Theoretical, Mathematical and Computational Physics
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Topological groups
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Topological groups, Lie groups
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Authors:
Dong, Chongying
.
Lepowsky, James
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Corporate Authors:
SpringerLink (Online service)
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Series:
Progress in mathematics
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Classification:
512
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