Witt型李超代数的Borel子代数

Borel subalgebras of Witt Lie superalgebras

设W是复数域上秩为3的有限维Witt型单李超代数。通过对正则元的分类,刻画关于典范环面的所有正根系,从而得到所有Borel子代数,进而确定相应的单根系;利用偶或奇本质反射和非本质反射,给出Borel子代数之间的邻接关系。结果可用于进一步研究Cartan型单李超代数的结构与表示。

Let plex numbers. All W be a finite-dimensional simple Witt Lie superalgebras of rank over the field of com- the positive root systems with respect to the standard torus are firstly characterized by means of classifying all the regular elements, and in particular all the Borel subalgebras with respect to the canonical torus are obtained. Then, all the simple root systems are determined and the adjacent relations between the Borel subalgebras are described by means of even or odd essential reflections and non- essential reflections. The results can be used in the further for studying the structure and representations of the finite-dimensional simple Cartan Lie superlagebras