Lie Higher Derivations on Triangular Algebras Revisited

F. Moafian, H.R. Ebrahimi Vishki

Motivated by the extensive works of W.-S. Cheung [Linear Multilinear Algebra, 51 (2003), 299--310] and X. F. Qi [Acta Math. Sinica, English Series, 29 (2013), 1007--1018], we present the structure of Lie higher derivations on a triangular algebra explicitly. We then study those conditions under which a Lie higher derivation on a triangular algebra is proper. Our approach provides a direct proof for some known results concerning to the properness of Lie higher derivations on triangular algebras.