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＜電子ブック＞
Generalized Vertex Algebras and Relative Vertex Operators / by Chongying Dong, James Lepowsky
(Progress in Mathematics. ISSN:2296505X ; 112)

版	1st ed. 1993.
出版者	(Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser)
出版年	1993
本文言語	英語
大きさ	IX, 206 p : online resource
著者標目	*Dong, Chongying author Lepowsky, James author SpringerLink (Online service)
件　名	LCSH:Algebra LCSH:Associative rings LCSH:Associative algebras LCSH:Operator theory LCSH:Group theory LCSH:Topological groups LCSH:Lie groups LCSH:Mathematical physics FREE:Algebra FREE:Associative Rings and Algebras FREE:Operator Theory FREE:Group Theory and Generalizations FREE:Topological Groups and Lie Groups FREE:Theoretical, Mathematical and Computational Physics
一般注記	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 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 generalof 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 HTTP:URL=https://doi.org/10.1007/978-1-4612-0353-7

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