Characterization of Lie higher derivations on triangular algebras.

Let $$\mathcal{A}$$ and $$\mathcal{B}$$ be unital rings, and $$\mathcal{M}$$ be an $$\left( {\mathcal{A},\mathcal{B}} \right)$$-bimodule, which is faithful as a left $$\mathcal{A}$$-module and also as a right $$\mathcal{B}$$-module. Let $$\mathcal{U} = Tri\left( {\mathcal{A},\mathcal{M},\mathcal{B}} \right)$$ be the triangular algebra. In this paper, we give some different characterizations of Lie higher derivations on $$\mathcal{U}$$. [ABSTRACT FROM AUTHOR]