可换环上一些上三角矩阵李代数的导子

Derivations of Certain Lie Algebras of Upper Triangular Matrices over Commutative Rings

中文关键词:  李代数的导子  可换环.

英文关键词:derivations of Lie algebras  commutative rings.

中文摘要:

      设$R$是任意含单位元的可换环, ${\bf t}$是$R$上$n\times n$上三角矩阵组成的李代数, $\bf{b}$是$R$上迹为零的$n\times n$上三角矩阵组成的李代数. 本文明确给出了${\bf t}$和$\bf{b}$ 的导子代数.

英文摘要:

      Let $R$ be an arbitrary commutative ring with identity. Denote by $\bf {t}$ the Lie algebra over $R$ consisting of all upper triangular $n$ by $n$ matrices and let $\bf{ b}$ be the Lie subalgebra of $\bf {t}$ consisting of all matrices of trace $0$. The aim of this paper is to give an explicit description of the derivation algebras of the Lie algebras $\bf{t}$ and $\bf{b}$, respectively.