Some categories of modules for toroidal Lie algebras

Abstract

In this paper, we use basic formal variable techniques to study certain categories of modules for the toroidal Lie algebra $\tau$. More specifically, we define and study two categories ${\mathcal{E}}_{\tau }$ and ${\mathcal{C}}_{\tau }$ of $\tau$-modules using generating functions, where ${\mathcal{E}}_{\tau }$ is proved to contain the evaluation modules while ${\mathcal{C}}_{\tau }$ contains certain restricted $\tau$-modules, the evaluation modules, and their tensor product modules. Furthermore, we classify the irreducible integrable modules in categories ${\mathcal{E}}_{\tau }$ and ${\mathcal{C}}_{\tau }$.

References in corpus (1)

• Representation theory and tensor product theory for vertex operator algebras