Lie Triple Derivations on Upper Triangular Matrices over a Commutative Ring

Abstract:

      Let ${\cal T}(n,R)$ be the Lie algebra consisting of all $n\times n$ upper triangular matrices over a commutative ring $R$ with identity $1$ and ${\cal M}$ be a $2$-torsion free unital ${\cal T}(n,R)$-bimodule. In this paper, we prove that every Lie triple derivation $d:{\cal T}(n,R)\rightarrow {\cal M}$ is the sum of a Jordan derivation and a central Lie triple derivation.