Some categories of modules for toroidal Lie algebras

In this paper, we use basic formal variable techniques to study certain categories of modules for the toroidal Lie algebra τ  . More specifically, we define and study two categories EτEτ and CτCτ of τ  -modules using generating functions, where EτEτ is proved to contain the evaluation modules while CτCτ contains certain restricted τ  -modules, the evaluation modules, and their tensor product modules. Furthermore, we classify the irreducible integrable modules in categories EτEτ and CτCτ.