Local and 2-local Lie n-derivations of triangular algebras

Abstract

Let R be a commutative ring with identity, and A , B be unital algebras over R . Let M be a unital ( A , B ) -bimodule, which is faithful as a left A -module and also as a right B -module. Let T = Tri ( A , M , B ) be an ( n − 1 ) -torsion free triangular algebra. In this note, we investigate the structure of local Lie n-derivations under certain mild conditions and 2-local Lie n-derivations under weaker conditions than that of local Lie n-derivations with n ≥ 3 on T . Under their corresponding conditions, we conclude that they are both standard on T .