TY - JOUR

T1 - Cohomology of conformal algebras

AU - Bakalov, Bojko

AU - Kac, Victor G.

AU - Voronov, Alexander A.

N1 - Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.

PY - 1999

Y1 - 1999

N2 - 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.

AB - 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.

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U2 - 10.1007/s002200050541

DO - 10.1007/s002200050541

M3 - Article

AN - SCOPUS:0033514097

VL - 200

SP - 561

EP - 598

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -