可换环上辛代数与一般线性李代数之间的中间李代数(英文)

INTERMEDIATE LIE ALGEBRAS BETWEEN THE SYMPLECTIC ALGEBRAS AND THE GENERAL LINEAR LIE ALGEBRAS OVER COMMUTATIVE RINGS

本文研究了含幺可换环上一般线性李代数的子代数结构.通过构造特殊矩阵并利用这些矩阵进行计算,得到了任意含幺可换环上辛代数与一般线性李代数之间的所有中间李代数的形式.并且有利于研究可换环上相应的典型群的子群结构.

In this paper, we study the subalgebra structure of the general linear Lie algebras over commutative rings. By constructing some special matrices and calculating, we obtain the forms of all intermediate Lie algebras between the symplectic algebras and the general linear Lie algebras over an arbitrary commutative rings with identity. This result will be helpful for us to know the subgroup structure of corresponding classical groups over commutative rings.