LR-algebras
Dietrich Burde, Karel Dekimpe, Sandra Deschamps

TL;DR
This paper investigates the existence and structure of LR-algebras on Lie algebras, establishing their connection to 2-step solvability and classifying low-dimensional cases.
Contribution
It provides criteria for the existence of LR-structures, explores their properties, and classifies low-dimensional real LR-algebras.
Findings
Any Lie algebra with an LR-structure is 2-step solvable.
Certain classes of 2-step solvable Lie algebras admit LR-structures.
Classification of low-dimensional real LR-algebras.
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.
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Taxonomy
TopicsAdvanced Topics in Algebra · Advanced Algebra and Logic · Fuzzy and Soft Set Theory
