Vertex algebras are algebraic structures that appear—often unexpectedly—in many areas of mathematics and physics. One of the central problems in the theory of vertex algebras is the construction of new and interesting examples.
In this talk, we present an approach to this problem known as the orbifold construction.
Given a vertex algebra V and a finite group of automorphisms G of V, the goal is to understand the representation theory of the fixed-point subalgebra V^G.
Foundational work on this topic was carried out in the 1990s by Chongying Dong and Geoffrey Mason, though it was limited to a very specific category of modules.
In this talk, we describe how this theory can be extended to arbitrary vertex algebra modules and provide examples of well-behaved module categories.
This lecture is based on joint work with Dražen Adamović, Ching-Hung Lam, and Nina Yu.
