Lie triple derivations and Jordan derivations of Hom-Lie algebra

Bing Sun and Liangyun Chen

Abstract

The paper studies generalized derivations of Hom-Lie algebras. More specifically speaking, (generalized) Lie triple (θ, ϕ)-derivations and (generalized) Jordan triple (θ, ϕ)-derivations on a Hom-Lie algebra are investigated. It is proved that Jordan triple (θ, ϕ)-derivations (resp. generalized Jordan triple (θ, ϕ)-derivations) are Lie triple (θ, ϕ)-derivations (resp. generalized Lie triple (θ, ϕ)-derivations) on a Hom-Lie algebra under some conditions. In particular, θ-Jordan derivations are Lie triple θ-derivations on a Hom-Lie algebra.