Overview
- Authors:
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Chongying Dong
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Department of Mathematics, University of California, Santa Cruz, Santa Cruz, USA
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James Lepowsky
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Department of Mathematics, Rutgers University, New Brunswick, USA
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About this book
In the past few years, vertex operator algebra theory has been growing both in intrinsic interest and in the scope of its interconnections with areas of mathematics and physics. The structure and representation theory of vertex operator algebras is deeply related to such subjects as monstrous moonshine, conformal field theory and braid group theory. Vertex operator algebras are the mathematical counterpart of chiral algebras in conformal field theory. In the Introduction which follows, we sketch some of the main themes in the historical development and mathematical and physical motivations of these ideas, and some of the current issues. Given a vertex operator algebra, it is important to consider not only its modules (representations) but also intertwining operators among the mod ules. Matrix coefficients of compositions of these operators, corresponding to certain kinds of correlation functions in conformal field theory, lead natu rally to braid group representations. In the specialbut important case when these braid group representations are one-dimensional, one can combine the modules and intertwining operators with the algebra to form a structure satisfying axioms fairly close to those for a vertex operator algebra. These are the structures which form the main theme of this monograph. Another treatment of similar structures has been given by Feingold, Frenkel and Ries (see the reference [FFR] in the Bibliography), and in fact the material de veloped in the present work has close connections with much work of other people, as we explain in the Introduction and throughout the text.
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Table of contents (14 chapters)
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- Chongying Dong, James Lepowsky
Pages 1-14
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- Chongying Dong, James Lepowsky
Pages 15-17
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- Chongying Dong, James Lepowsky
Pages 19-25
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- Chongying Dong, James Lepowsky
Pages 27-31
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- Chongying Dong, James Lepowsky
Pages 33-47
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- Chongying Dong, James Lepowsky
Pages 49-58
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- Chongying Dong, James Lepowsky
Pages 59-75
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- Chongying Dong, James Lepowsky
Pages 77-81
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- Chongying Dong, James Lepowsky
Pages 83-94
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- Chongying Dong, James Lepowsky
Pages 95-96
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- Chongying Dong, James Lepowsky
Pages 97-104
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- Chongying Dong, James Lepowsky
Pages 105-140
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- Chongying Dong, James Lepowsky
Pages 141-160
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- Chongying Dong, James Lepowsky
Pages 161-189
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Back Matter
Pages 191-206
Reviews
"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
Authors and Affiliations
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Department of Mathematics, University of California, Santa Cruz, Santa Cruz, USA
Chongying Dong
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Department of Mathematics, Rutgers University, New Brunswick, USA
James Lepowsky