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An operadic approach to vertex algebra and Poisson vertex algebra cohomology
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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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Double Poisson (vertex) algebra cohomology
The authors define a completed double Poisson cohomology valid for all double Poisson brackets, and introduce three cohomology theories for double Poisson vertex algebras, with representation functor compatibility.
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