LR-algebras

2008/01/08 by Burde, Dietrich, Dekimpe, Karel, Deschamps, Sandra
#17B30 #17D25 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.0801.1280

Abstract

In the study of NIL-affine actions on nilpotent Lie groups we introduced so called LR-structures on Lie algebras. The aim of this paper is to consider the existence question of LR-structures, and to start a structure theory of LR-algebras. We show that any Lie algebra admitting an LR-structure is 2-step solvable. Conversely we find several classes of 2-step solvable Lie algebras admitting an LR-structure, but also classes not admitting such a structure. We study also ideals in LR-algebras, and classify low-dimensional real LR-algebras.

Related

• Complete LR-structures on solvable Lie algebras
• Affine actions on Lie groups and post-Lie algebra structures
• Post-Lie algebra structures on pairs of Lie algebras
• On post-Lie algebras structures coming from simply transitive NIL-affine actions
• Post-Lie algebra structures for nilpotent Lie algebras