2021 article
Classical and variational Poisson cohomology
Bakalov, B., De Sole, A., Heluani, R., Kac, V. G., & Vignoli, V. (2021, August 9). JAPANESE JOURNAL OF MATHEMATICS.
author keywords: Poisson vertex algebra (PVA); classical operad; classical PVA cohomology; variational PVA cohomology; sesquilinear Hochschild and Harrison cohomology
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14. Life Below Water
(Web of Science)
Source: Web Of Science
Added: August 16, 2021
We prove that, for a Poisson vertex algebra $${\cal V}$$ , the canonical injective homomorphism of the variational cohomology of $${\cal V}$$ to its classical cohomology is an isomorphism, provided that $${\cal V}$$ , viewed as a differential algebra, is an algebra of differential polynomials in finitely many differential variables. This theorem is one of the key ingredients in the computation of vertex algebra cohomology. For its proof, we introduce the sesquilinear Hochschild and Harrison cohomology complexes and prove a vanishing theorem for the symmetric sesquilinear Harrison cohomology of the algebra of differential polynomials in finitely many differential variables.