模李超代数研究的若干进展

Some Advances of the Researches on Modular Lie Superalgebras

近几年,模李超代数（即素特征域上的李超代数）的研究取得了一些进展.本文分以下6个方面介绍近几年在模李超代数研究中取得的一些新结果.1.限制李超代数;2.Cartan型模李超代数;3.深度1的Z-阶化李超代数;4.深度1的滤过李超代数;5.Cartan型模李超代数的某些内蕴性质;6.公开的问题.

In recent years, there are some advances in the study on the modular Lie su-peralgebras. In this paper, the following aspects of these advances are presented: the restricted Lie superalgebras, modular Lie superalgebras of Cartan type and their some intrinsic properties, Z-graded Lie superalgebras and filtered Lie superalgebras with depth one. Finally some open problems are proposed.