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

Abstract:

      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.