Computation of cohomology of Lie conformal and Poisson vertex algebras

Alberto De Sole; Bojko Bakalov; Victor G. Kac

Computation of cohomology of Lie conformal and Poisson vertex algebras

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arxiv 1903.12059 v2 pith:SVPN4EGQ submitted 2019-03-28 math.RT math-phmath.MP

Bojko Bakalov , Alberto De Sole , Victor G. Kac This is my paper · ORCID

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keywords poissonvertexalgebrascohomologyconformalcomputationsuperaffine

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We develop methods for computation of Poisson vertex algebra cohomology. This cohomology is computed for the free bosonic and fermionic Poisson vertex (super)algebras, as well as for the universal affine and Virasoro Poisson vertex algebras. We establish finite dimensionality of this cohomology for conformal Poisson vertex (super)algebras that are finitely and freely generated by elements of positive conformal weight.

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Double Poisson (vertex) algebra cohomology
math.RT 2025-09 accept novelty 8.0 of 10

The authors define a completed double Poisson cohomology valid for all double Poisson brackets, and introduce three cohomology theories for double Poisson vertex algebras, with representation functor compatibility.

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