Generalized Lie derivations on triangular algebras

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Let A be a unital algebra and let M be a unitary A -bimodule. We consider generalized Lie derivations mapping from A to M . Our results are applied to triangular algebras, in particular to nest algebras and (block) upper triangular matrix algebras. We prove that under certain conditions each generalized Lie derivation of a triangular algebra A is the sum of a generalized derivation and a central map which vanishes on all commutators of A .