Generalized Vertex Algebras and Relative Vertex Operators: v. 112 (Progress in Mathematics) - Hardcover

Dong, Chongying; Lepowsky, James

Hardcover

ISBN 10: 3764337214 ISBN 13: 9783764337216

Publisher: Birkhauser Verlag AG, 1993

Synopsis

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 present a generalization of the theory of vertex operator algebras in a systematic way, in three successive stages, all of which involve one-dimensional braid group representations intrinsically in the algebraic structure: First, their notion of "generalized vertex operator algebra" incorporates such structures as Z-algebras, parafermion algebras, and vertex operator superalgebras. Important examples are based on a general construction that they cau "relative vertex operators." Next, what they term "generalized vertex algebras' encompass in addition the algebras of vertex operators associated with rational lattices. Finally, the most general of the three notions, that of 'abelian intertwining algebra," also iuun-iinates the theory of intertwining operators for certain classes of vertex operator algebras. The monograph is written in an accessible and self-contained way, with detailed proofs and with many examples interwoven through the axiomatic treatment as motivation and applications. It win be useful for research mathematicians and theoretical physicists working in such fields as representation theory and algebraic structures and will provide the basis for a number of graduate courses and seminars on these and related topics.

About this title

Review

"The presentation is smooth, self-contained and accessible with detailed proofs. The introduction offers background and history about the generalized theory. It also uses examples to show some of the central techniques in VOA, thus offering pedagogical help to the readers. I think this book will benefit researchers in the field."

―Mathematical Reviews

Edition details

• Publisher: Birkhauser Verlag AG
• Publication date: 1993
• Language: English
• ISBN 10: 3764337214
• ISBN 13: 9783764337216
• Binding: Hardcover
• Number of pages: 208