On the Lie triple derivations

Abstract

This article aims to interpret some Lie triple derivations of Tensor algebras , using generalized quaternion algebra over a field F and assuming T as an F-linear associative algebra. The study concludes with complete description of all Lie triple derivations of A ⊗ F L. It is pertinent to mention here that A is assumed to be a finite-dimensional commutative algebra and L is a simple Lie algebra over an algebraically closed field.