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Generalized Vertex Algebras and Relative Vertex Operators

  • Chongying Dong
  • James Lepowsky

Part of the Progress in Mathematics book series (PM, volume 112)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Chongying Dong, James Lepowsky
    Pages 1-14
  3. Chongying Dong, James Lepowsky
    Pages 15-17
  4. Chongying Dong, James Lepowsky
    Pages 19-25
  5. Chongying Dong, James Lepowsky
    Pages 27-31
  6. Chongying Dong, James Lepowsky
    Pages 33-47
  7. Chongying Dong, James Lepowsky
    Pages 49-58
  8. Chongying Dong, James Lepowsky
    Pages 59-75
  9. Chongying Dong, James Lepowsky
    Pages 77-81
  10. Chongying Dong, James Lepowsky
    Pages 83-94
  11. Chongying Dong, James Lepowsky
    Pages 95-96
  12. Chongying Dong, James Lepowsky
    Pages 97-104
  13. Chongying Dong, James Lepowsky
    Pages 105-140
  14. Chongying Dong, James Lepowsky
    Pages 141-160
  15. Chongying Dong, James Lepowsky
    Pages 161-189
  16. Back Matter
    Pages 191-206

About this book

Introduction

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.

Keywords

Algebraic structure Cohomology Lattice Representation theory algebra cls homology ring theory

Authors and affiliations

  • Chongying Dong
    • 1
  • James Lepowsky
    • 2
  1. 1.Department of MathematicsUniversity of California, Santa CruzSanta CruzUSA
  2. 2.Department of MathematicsRutgers UniversityNew BrunswickUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-0353-7
  • Copyright Information Birkhäuser Boston 1993
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6721-8
  • Online ISBN 978-1-4612-0353-7
  • Series Print ISSN 0743-1643
  • Series Online ISSN 2296-505X
  • Buy this book on publisher's site
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