2014/11/04 by Burde, Dietrich
#FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.1411.0950
We study classical R-matrices D for Lie algebras L such that D is also a derivation of L. This yields derivation double Lie algebras (L,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.