Cohomology of Conformal Algebras

Details Cohomology of Conformal Algebras Cohomology of Conformal Algebras

1998-03-07

arxiv.org/abs/math/9803022v2

Commun.Math.Phys. 200 (1999) 561-598

Mathematics

Quantum Algebra

46 pp., AMSLaTeX, uses epsfig, amssymb, amscd

Scientific paper

10.1007/s002200050541

Conformal algebra is 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, like the Virasoro algebra and loop algebras. In the present paper we develop a cohomology theory of conformal algebras with coefficients in an arbitrary module. It possesses standard properties of cohomology theories; for example, it describes extensions and deformations. We offer explicit computations for most of the important examples.

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