# An operadic approach to vertex algebra and Poisson vertex algebra cohomology

@article{Bakalov2018AnOA, title={An operadic approach to vertex algebra and Poisson vertex algebra cohomology}, author={Bojko Bakalov and Alberto De Sole and Reimundo Heluani and Victor G. Kac}, journal={Japanese Journal of Mathematics}, year={2018}, volume={14}, pages={249-342} }

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 the vertex algebra cohomology complex. Likewise, the associated graded of the chiral operad leads to the classical operad, which produces a Poisson vertex algebra cohomology complex. The latter is closely related to the variational Poisson cohomology studied by two… CONTINUE READING

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## Chiral algebras

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## Examples of Algebraic Operads

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