Following Beilinson and Drinfeld, we describe vertex algebras as Lie algebras for a certain operad of n-ary chiral operations. This allows us to introduce the cohomology of a vertex algebra V as a
Lie algebra cohomology. When V is equipped with a good filtration, its associated graded is a Poisson vertex algebra. We relate the cohomology of V to the variational Poisson cohomology studied previously by De Sole and Kac.
This talk is based on joint work with Alberto De Sole, Reimundo Heluani, Victor Kac, and Veronica Vignoli.
This video was part of the Southeastern Lie Theory Workshop XII.
