ON LEVI’S THEOREM FOR LEIBNIZ ALGEBRAS

By D. W. Barnes. Bulletin of the Australian Mathematical Society, 2011

148 citations recorded by the source corpus.

Abstract A Lie algebra over a field of characteristic 0 splits over its soluble radical and all complements are conjugate. I show that the splitting theorem extends to Leibniz algebras but that the conjugacy theorem does not.

Subfields: Algebra and Number Theory, Geometry and Topology, Polymers and Plastics

View Paper: https://www.semanticscholar.org/paper/6c44e81c1451ae5f8e761cd50840b24a6fb4e32b

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Citations in the corpus

Classification of solvable Leibniz algebras with naturally graded filiform nilradical (2012, methodology): “Of course, distinctive properties of non-Lie Leibniz algebras have also been studied [4,5].”
The classification of 4-dimensional Leibniz algebras (2013, background): “lradicals comes from diﬀerent problems in Physics and was the subject of various paper [4, 8, 10, 15, 19, 20]. In Leibniz algebras, the analogue of Levi-Malcev’s theorem was proved in recent times in [7], thus solvable Leibniz algebras still play a central role and have been recently studied by seve”
ON SOME STRUCTURES OF LEIBNIZ ALGEBRAS (2013, background): “However, as shown in [9] Malcev’s congugacy theorem does not hold for Leibniz algebras.”
Classification of solvable Leibniz algebras with null-filiform nilradical (2012, background): “potent ones. Thus, the description of ﬁnite-dimensional Lie algebras is reduced to the description of nilpotent algebras. In the case of Leibniz algebras, the analogue of Levi’s theorem was proven in [6]. Namely, a Leibniz algebra is decomposed into a semidirect sum of the solvable radical and a sem”