Lie triple derivations of triangular algebras

Let R be a commutative ring with identity, A, B be unital algebras over R and M be a unital (A, B)-bimodule. which is faithful as a left A-module and also as a right B-module. Let T = [(A)(0) (M)(B)] be the triangular algebra consisting of A, B and M. This work is motivated by some intensive works of Bre ar [4], Cheung [9] and Zhang et al. [30]. Here, we study Lie triple derivations of T. It is shown that under mild assumptions, every Lie triple derivation on T is of standard form. That is, L can be expressed through an additive derivation and a linear functional vanishing on all second commutators of T. Examples of Lie triple derivations on some classical triangular algebras are supplied. (C) 2012 Elsevier Inc. All rights reserved.