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.

仿射和环形李代数的表示理论中的一个重要问题是用有限维权空间对所有可能的不可约可积模块进行分类。最近，具有更重要的中心作用的具有有限维权空间的不可约可积模块已被分类为更一般的李代数，即分级的李托里。在本文中，我们对这个分级的李托里的所有不可约可积模块进行了有限维权重空间的分类，其中中心元素起着微不足道的作用。因此，我们最终获得了分级Lie tori的具有有限维权空间的可积模块类别中的所有简单对象。