Categorification of Virasoro–Magri Poisson vertex algebra

Categorification and Groupoidification of the Heisenberg Algebra

These lectures, prepared for Higher Structures in China III, held in Changchun, Aug 2012, describe a relationship between two forms of categorification of algebras by giving a combinatorial model for Khovanov’s categorification of the Heisenberg algebra in a 2-category of spans of groupoids. This is joint work with Jamie Vicary. The goal here is to describe two notions of “categorifying an alge...

Vertex algebras and vertex poisson algebras

This paper studies certain relations among vertex algebras, vertex Lie algebras and vertex poisson algebras. In this paper, the notions of vertex Lie algebra (conformal algebra) and vertex poisson algebra are revisited and certain general construction theorems of vertex poisson algebras are given. A notion of filtered vertex algebra is formulated in terms of a notion of good filtration and it i...

Vertex Lie algebras, vertex Poisson algebras and vertex algebras

The notions of vertex Lie algebra and vertex Poisson algebra are presented and connections among vertex Lie algebras, vertex Poisson algebras and vertex algebras are discussed.

Vertex Operator Algebra Structure of Standard Affine Lie Algebra Modules

Melikyan algebra is a deformation of a Poisson algebra

We prove, using computer, that the restricted Melikyan algebra of dimension 125 is a deformation of a Poisson algebra.