有限维权空间分次李环面的可积模
Integrable Modules For Graded Lie Tori With Finite Dimensional Weight Spaces
摘要：
仿射和环面李代数表示论中的一个重要问题是对所有可能的具有有限维权空间的不可约可积模进行分类。最近，具有非平凡中心作用的有限维权空间的不可约可积模被分类为一类更一般的李代数，即分次李环面。本文对这种分次李环面的中心元平凡作用的有限维权空间的不可约可积模进行了分类。这样，我们最终得到了分次李环面上具有有限维权空间的可积模范畴中的所有简单对象。
英文摘要：
An important problem in the representation theory of affine and toroidal Lie algebras is to classify all possible irreducible integrable modules with finite dimensional weight spaces. Recently the irreducible integrable modules having finite dimensional weight spaces with non-trivial central action have been classified for a more general class of Lie algebras, namely the graded Lie tori. In this paper, we classify all the irreducible integrable modules with finite dimensional weight spaces for this graded Lie tori where the central elements act trivially. Thus we ultimately obtain all the simple objects in the category of integrable modules with finite dimensional weight spaces for the graded Lie tori.
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