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LR-algebras. (English) Zbl 1251.17003

Gordon, Carolyn S. (ed.) et al., New developments in Lie theory and geometry. Proceedings of the 6th workshop on Lie theory and geometry, Cruz Chica, C√≥rdoba, Argentina, November 13–17, 2007. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4651-3/pbk). Contemporary Mathematics 491, 125-140 (2009).
Summary: 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.
For the entire collection see [Zbl 1170.22002].

MSC:

17B30 Solvable, nilpotent (super)algebras
17D25 Lie-admissible algebras
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