Lie Triple Derivations Of The Parabolic Subalgebras Of The General Linear Lie Algebra Over A Commutative Ring

Let R be a commutative ring with identity and Ann(2) = 0,gl(n, R) be the generallinear Lie algebra consisting of all n×n matrices over R.The main aim of this paper is as follows:(1) give the standard Lie triple derivations of parabolic subalgebras of gl(n, R);(2) decompose every Lie triple derivation of a parabolic subalgebra of gl(n, R) into asum of standard Lie triple derivations and discuss the uniqueness of the decomposition.