TY - JOUR
T1 - Cohomology of conformal algebras
AU - Bakalov, Bojko
AU - Kac, Victor G.
AU - Voronov, Alexander A.
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
SN - 0010-3616
VL - 200
SP - 561
EP - 598
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 3
ER -