  An LR-structure on a Lie algebra is a bilinear product, satisfying certain
commutativity relations, and which is compatible with the Lie product.
LR-structures arise in the study of simply transitive affine actions on Lie
groups. In particular one is interested in the question which Lie algebras
admit a complete LR-structure. In this paper we show that a Lie algebra admits
a complete LR-structure if and only if it admits any LR-structure.

Rings and Algebras;Differential Geometry