# Additive Lie $ξ$-Lie Derivations and Generalized Lie $ξ$-Lie Derivations on Prime Algebras - Mathematics > Operator Algebras

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Abstract: The additive generalized $\xi$-Lie derivations on prime algebras arecharacterized. It is shown, under some suitable assumption, that an additivemap $L$ is an additive generalized Lie derivation if and only if it is thesum of an additive generalized derivation and an additive map from thealgebra into its center vanishing all commutators; is an additive generalized$\xi$-Lie derivation with $\xi ot=1$ if and only if it is an additivegeneralized derivation satisfying $L\xi A=\xi LA$ for all $A$. Theseresults are then used to characterize additive generalized $\xi$-Liederivations on several operator algebras such as Banach space standard operatoralgebras and von Neumman algebras.

Autor: Xiaofei Qi, Jinchuan Hou

Fuente: https://arxiv.org/