Yi-Zhi Huang
Vertex operator algebras and tensor categories
Two-dimensional conformal field theory can be studied using the representation theory of vertex operator algebras. Suitable module categories for vertex operator algebras have structures of vertex tensor categories. These vertex tensor categories give braided tensor categories and, when the vertex operator algebras satisfy strong conditions, give modular tensor categories.
In this course, I will discuss the construction of these vertex tensor categories and braided tensor categories. Below are the detailed topics to be covered in this course:
1. Vertex operator algebras, modules and intertwining operators.
2. Tensor product modules and their construction.
3. Associativity of intertwining operators and associativity isomorphisms.
4. Skew-symmetry and commutativity of intertwining operators and braiding isomorphisms.
5. Vertex tensor categories and braided tensor categories.
6. Rigidity, twists and modularity.
No text book. Lectures are based on papers and lecture notes that are available online.
First year graduate algebra and analysis courses.