Cohomology of conformal algebras

Bojko Bakalov, Victor G. Kac, Alexander A. Voronov

Research output: Contribution to journalArticle

75 Scopus citations

Abstract

The notion of a conformal algebra encodes an axiomatic description of the operator product expansion of chiral fields in conformal field theory. On the other hand, it is an adequate tool for the study of infinite-dimensional Lie algebras satisfying the locality property. The main examples of such Lie algebras are those "based" on the punctured complex plane, such as the Virasoro algebra and loop Lie algebras. In the present paper we develop a cohomology theory of conformal algebras with coefficients in an arbitrary module. It possesses standards properties of cohomology theories; for example, it describes extensions and deformations. We offer explicit computations for the most important examples.

Original languageEnglish (US)
Pages (from-to)561-598
Number of pages38
JournalCommunications in Mathematical Physics
Volume200
Issue number3
DOIs
StatePublished - Jan 1 1999

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