Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Representations of Affine and Toroidal Lie Algebras   We discuss the category $\cal I$ of level zero integrable representations of
loop algebras and their generalizations. The category is not semisimple and so
one is interested in its homological properties. We begin by looking at some
approaches which are used in the study of other well--known non--semisimple
categories in the representation theory of Lie algebras. This is done with a
view to seeing if and how far these approaches can be made to work for $\cal
I$. In the later sections we focus first on understanding the irreducible level
zero modules and later on certain universal modules, the local and global Weyl
modules which in many ways play a role similar to the Verma modules in the
BGG--category $\cal O$. In the last section, we discuss the connections with
the representation theory of finite--dimensional associative algebras and on
some recent work with J. Greenstein.

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The categories of this paper are: q-bio
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The categories of this paper are: physics
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The categories of this paper are: nlin
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The categories of this paper are: stat
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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: cs
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The categories of this paper are: nucl-th