I will start by reviewing the notions of vertex algebra, Poisson vertex algebra, and Lie conformal algebra, and their relations to each other. Then I will present a unified approach to all these algebras as Lie algebras in certain pseudo-tensor categories, or equivalently, as morphisms from the Lie operad to certain operads. As an application, I will introduce a cohomology theory of vertex algebras similarly to Lie algebra cohomology, and will show how it relates to the cohomology of Poisson vertex algebras and of Lie conformal algebras.
The talk is based on joint work with Alberto De Sole, Reimundo Heluani, Victor Kac, and Veronica Vignoli.
This video was produced by the Universidade de São Paulo, as part of the LieJor Online Seminar: Algebras, Representations, and Applications.
