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arXiv · 1806.08754

An operadic approach to vertex algebra and Poisson vertex algebra cohomology

Bojko Bakalov·Alberto De Sole·Reimundo Heluani·Victor G. Kac
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Abstract

We translate the construction of the chiral operad by Beilinson and Drinfeld to the purely algebraic language of vertex algebras. Consequently, the general construction of a cohomology complex associated to a linear operad produces a vertex algebra cohomology complex. Likewise, the associated graded of the chiral operad leads to a classical operad, which produces a Poisson vertex algebra cohomology complex. The latter is closely related to the variational Poisson cohomology studied by two of the authors.

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Bojko Bakalov, Alberto De Sole, Reimundo Heluani, Victor G. Kac. 2018-06-22. An operadic approach to vertex algebra and Poisson vertex algebra cohomology. https://doi.org/10.1007/s11537-019-1825-3

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