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ON LEVI’S THEOREM FOR LEIBNIZ ALGEBRAS

Published online by Cambridge University Press:  30 November 2011

DONALD W. BARNES*
Affiliation:
1 Little Wonga Rd, Cremorne, NSW 2090, Australia (email: [email protected])
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Abstract

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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.

MSC classification

Type
Research Article
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

References

[1]Ayupov, Sh. A. and Omirov, B. A., ‘On Leibniz algebras’, in: Algebra and Operators Theory, Proceedings of the Colloquium in Tashkent (Kluwer, Dordrecht, 1998), pp. 113.Google Scholar
[2]Jacobson, N., Lie Algebras (Interscience, New York–London, 1962).Google Scholar
[3]Loday, J.-L. and Pirashvili, T., ‘Leibniz representations of Lie algebras’, J. Algebra 181 (1996), 414425.CrossRefGoogle Scholar
[4]Patsourakos, A., ‘On nilpotent properties of Leibniz algebras’, Comm. Algebra 35 (2007), 38283834.CrossRefGoogle Scholar