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 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.

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

Cited by in corpus (31)

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• Classification of finite irreducible conformal modules over some Lie conformal algebras related to the Virasoro conformal algebra
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• 2-Cocycles of Original Deformative Schrödinger-Virasoro Algebras
• Jacobi Identity for Vertex Algebras in Higher Dimensions
• Conformal classical Yang-Baxter equation, $S$-equation and $\mathcal{O}$-operators
• Extending structures for associative conformal algebras
• Loop Heisenberg-Virasoro Lie Conformal algebra
• An operadic approach to vertex algebra and Poisson vertex algebra cohomology
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• Universal enveloping Poisson conformal algebras
• Boundary Conformal Field Theories, Limit Sets of Kleinian Groups and Holography
• Infinite rank Schrodinger-Virasoro type Lie conformal algebras
• On the Ado Theorem for finite Lie conformal algebras with Levi decomposition
• Deformations and generalized derivations of Lie conformal superalgebras
• Deformations and generalized derivations of Hom-Lie conformal algebras
• Computation of cohomology of Lie conformal and Poisson vertex algebras
• Extensions of Schrödinger-Virasoro conformal modules
• Calculus structure on the Lie conformal algebra complex and the variational complex
• A remark on simplicity of vertex algebras and Lie conformal algebras
• Finite vertex algebras and nilpotence
• Hochshild cohomology of the associative conformal algebra Cend_{1,x}
• Finite irreducible conformal modules over the Lie conformal superalgebra $\mathcal{S}(p)$
• Conformal $r$-matrix-Nijenhuis structures, symplectic-Nijenhuis structures and $\mathcal{O}N$-structures
• Standard bases for the universal associative conformal envelopes of Kac--Moody conformal algebras
• Hochschild cohomology of the Weyl conformal algebra with coefficients in finite modules