  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.

Quantum Algebra