有限Chevalley群作用下的子代数轨道生成的格

Lattices Generated by Transitive Sets of Subalgebras under Finite Chevalley Groups

讨论了一般情形Chevalley群作用下的子代数轨道生成的格.在同类型格中,研究了不同格之间的包含关系,并对格中子代数的特性及格的几何性进行了刻画.

This paper is to study the lattices generated by transitive sets of subalgebras under general Chevalley groups over finite fields. At first, we shall study the inclusion relations between the lattices of the same type. Then we shall give a characterization of subalgebras contained in a given lattices. Finally, we shall describe the geometry properties of the lattices.