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ON LEVI’S THEOREM FOR LEIBNIZ ALGEBRAS

  • DONALD W. BARNES (a1)
Abstract
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.

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[1]Sh. A. Ayupov and B. A. Omirov , ‘On Leibniz algebras’, in: Algebra and Operators Theory, Proceedings of the Colloquium in Tashkent (Kluwer, Dordrecht, 1998), pp. 113.

[3]J.-L. Loday and T. Pirashvili , ‘Leibniz representations of Lie algebras’, J. Algebra 181 (1996), 414425.

[4]A. Patsourakos , ‘On nilpotent properties of Leibniz algebras’, Comm. Algebra 35 (2007), 38283834.

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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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