Derivation double Lie algebras

摘要

We study classical R-matrices D for Lie algebras g such that D is also a derivation of g. This yields derivation double Lie algebras (g, D). The motivation comes from recent work on post-Lie algebra structures on pairs of Lie algebras arising in the study of nil-affine actions of Lie groups. We prove that there are no nontrivial simple derivation double Lie algebras, and study related Lie algebra identities for arbitrary Lie algebras.