On generalized Lie derivations
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In this paper, we investigate generalized Lie derivations. We give a complete characterization of when each generalized Lie derivation is a sum of a generalized inner derivation and a Lie derivation. This generalizes a result given by Benkovič. We also investigate when every generalized Lie derivation on some particular kind of unital algebras is a sum of a generalized derivation and a central map which vanishes on all commutators. Precisely, we consider both the unital algebras with nontrivial idempotents and the trivial extension algebras.
KeywordsGeneralized Lie derivation Trivial extension algebra Triangular algebra
Mathematics Subject Classification47B47 15A78 16W25
The authors would like to thank the referee for careful reading of the manuscript.