Characterization Of Lie Higher Derivations On Algebras

In this paper, Lie higher derivations on algebras are investigated and the properties of these derivations are analyzed and characterized. Let JA be algebra and D=(Li)i∈N be a sequence of linear maps on A such that Lo=idA. D is called a Lie higher derivation if for each x, y∈A and each non-negative integer n∈N. We show that if{Ln} is a Lie higher derivation on an algebra A such that Lo is the identity mapping on A, then there is a sequence{L’n} of Lie derivations on A such that where the inner summation is taken over all positive integers rj with...