The W3 Algebra

Modules, Semi-infinite Cohomology and BV Algebras

  • Peter Bouwknegt
  • Jim McCarthy
  • Krzysztof Pilch

Part of the Lecture Notes in Physics Monographs book series (LNPMGR, volume 42)

Table of contents

  1. Front Matter
    Pages I-XI
  2. Back Matter
    Pages 149-204

About this book


W algebras are nonlinear generalizations of Lie algebras that arise in the context of two-dimensional conformal field theories when one explores higher-spin extensions of the Virasoro algebra. They provide the underlying symmetry algebra of certain string generalizations which allow the extended world sheet gravity. This book presents such gravity theories, concentrating on the algebra of physical operators determined from an analysis of the corresponding BRST cohomology. It develops the representation theory of W algebras needed to extend the standard techniques which were so successful in treating linear algebras. For certain strings corresponding to WN gravity we show that the operator cohomology has a natural geometric model. This result suggests new directions for the study of W geometry.


Virasaro algebra W*-geometry algebra cohomology field geometry gravity lie algebra linear algebra quantum gravity representation theory

Authors and affiliations

  • Peter Bouwknegt
    • 1
  • Jim McCarthy
    • 1
  • Krzysztof Pilch
    • 2
  1. 1.Department of Physics and Mathematical PhysicsUniversity of AdelaideAdelaideAustralia
  2. 2.Department of Physics and AstronomyUniversity of Southern CaliforniaLos AngelesUSA

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1996
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-61528-6
  • Online ISBN 978-3-540-68719-1
  • Series Print ISSN 0940-7677
  • Buy this book on publisher's site
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