2020 journal article

Computation of cohomology of Lie conformal and Poisson vertex algebras

SELECTA MATHEMATICA-NEW SERIES, 26(4).

By: B. Bakalov n, A. De Sole * & V. Kac*

author keywords: Lie conformal (super)algebras; Poisson vertex (super)algebras; Affine Lie algebras; Virasoro algebra; Basic cohomology; LCA cohomology; Variational PVA cohomology; Energy operator
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14. Life Below Water (Web of Science)
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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.