R-典型线性李代数为R-单李代数的充要条件

The Necessary and Sufficient Condition on Which the R-classical Linear Lie Algebra is R-simple Lie Algebra

由于域上的典型线性李代数都是单李代数,而交换幺环上的典型线性李代数未必仍为单李代数,而单李代数的结构分类对研究半单纯李代数的结构分类,以及可解、幂零李代数的研究至关重要,在这里我们得出了交换幺环上典型线性李代数为R-单李代数的充要条件。

Because the classical linear Lie algebra over a field is a simple Lie algebra, but the classical linear Lie algebra over a ring with identity may not still be a simple Lie algebra, and the classification and structure of simple Lie algebras is critical to the study of the the structure and classification of the semi-simple Lie algebra, even solvable, nilpotent Lie algebra, here we give the necessary and sufficient condition on which the R-classical linear Lie algebra is R-simple Lie algebra.