Derivations of Certain Linear Lie Algebras over Commutative Rings

Abstract:

      Let $L$ be the symplectic algebra or the orthogonal algebra over a commutative ring $R$, $h$ the maximal torus of $L$ consisting of all diagonal matrices in $L$, and $b$ the standard Borel subalgebra of $L$ containing $h$. In this paper, we first determine the intermediate algebras between $h$ and $b$, then for such an intermediate algebra, we give an explicit description on its derivations, provided that $R$ is a commutative ring with identity and $2$ is invertible in $R$.