An operadic approach to vertex algebra and Poisson vertex algebra cohomology

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.

72 pages, in the second version we corrected the part related to the cohomology of the free boson (Sec.11.3) and some other minor errors

References in corpus (3)

• Deformations of chiral algebras
• Deformation quantization of vertex Poisson algebras
• The Bernstein-Sato $b$-function of the Vandermonde determinant

Cited by in corpus (2)

• Computation of cohomology of Lie conformal and Poisson vertex algebras
• Chiral vs classical operad