Introduction to Vertex Operator Algebras

Teacher :Robert McRae
Schedule: Tue & Fri 09:50-11:25, 2020-2-18 ~ 5-8
Venue:Conference Room 1, Jin Chun Yuan West Bldg.


Vertex operator algebras are an algebraic tool for the rigorous mathematical study of two-dimensional conformal quantum field theory. In this course, we will focus on the definition, axioms, and examples of vertex operator algebras and their representations. If time permits, we will also introduce the representation theory of vertex operator algebras, with topics including intertwining operators and tensor categories of modules.


Graduate-level abstract algebra and complex analysis. Some familiarity with Lie algebras would also be helpful but not essential.


The course material will be selected from the following references:

Introduction to Vertex Operator Algebras and Their Representations by James Lepowsky and Haisheng Li

Vertex Operator Algebras and the Monster by Igor Frenkel, James Lepowsky, and Arne Meurman

On axiomatic approaches to vertex operator algebras and modules by Igor Frenkel, Yi-Zhi Huang, and James Lepowsky

Logarithmic tensor category theory for generalized modules for a conformal vertex algebra by Yi-Zhi Huang, James Lepowsky, and Lin Zhang


Some additional references on vertex operator algebras:

Vertex Algebras for Beginners by Victor Kac

Vertex Algebras and Algebraic Curves by David Ben-Zvi and Edward Frenkel