论文标题
具有有限尺寸重量空间的分级谎言托里的可集成模块
Integrable Modules For Graded Lie Tori With Finite Dimensional Weight Spaces
论文作者
论文摘要
仿射和环形谎言代数的表示理论中的一个重要问题是，用有限的维度重量空间对所有可能的不可约合模块进行分类。最近，具有有限的尺寸重量空间具有非平凡的中央作用的不可约合的集成模块已被分类为更一般的Lie代数类别，即分级的Lie Tori。在本文中，我们将所有不可约合的集成模块与有限的尺寸重量空间进行分类，用于该分级的Lie Tori，其中中央元素在琐碎的作用。因此，我们最终在具有有限的尺寸重量空间的可集成模块类别中获取所有简单对象。
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.
