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Register a new userSome categories of modules for toroidal Lie algebras
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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 $mathcal{C}_{tau}$.
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