Cohomology of Conformal Algebras
Abstract
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 infinitedimensional 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.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 1999
 DOI:
 10.1007/s002200050541
 arXiv:
 arXiv:math/9803022
 Bibcode:
 1999CMaPh.200..561B
 Keywords:

 Mathematics  Quantum Algebra
 EPrint:
 46 pp., AMSLaTeX, uses epsfig, amssymb, amscd