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Zhu algebras for vertex operator algebras

Algebraic Geometry Seminar

Zhu algebras for vertex operator algebras
Series: Algebraic Geometry Seminar
Location: Online,
Presenter: Darlayne Addabbo, University of Arizona

Given a vertex operator algebra, $V$, there is a family of associative algebras, $A_n(V)$, $n\in \mathbb{N}$, known as Zhu algebras, which can be used to study the representation theory of $V$. In this talk, I will define these Zhu algebras and discuss motivation for their study. I will then discuss techniques used in determining their structure and give an example clarifying the necessity of certain conditions in defining the Zhu algebras, $A_n(V)$ for $n>0$. I will not assume prior knowledge of vertex operator algebras. (This is joint work with Katrina Barron.)