2020 journal article
Computation of cohomology of Lie conformal and Poisson vertex algebras
SELECTA MATHEMATICA-NEW SERIES, 26(4).
author keywords: Lie conformal (super)algebras; Poisson vertex (super)algebras; Affine Lie algebras; Virasoro algebra; Basic cohomology; LCA cohomology; Variational PVA cohomology; Energy operator
open access via arxiv.org (repository)
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Added: July 27, 2020
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.