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ON LEVI’S THEOREM FOR LEIBNIZ ALGEBRAS

Part of: General nonassociative rings

Published online by Cambridge University Press:  30 November 2011

DONALD W. BARNES
DONALD W. BARNES*
Affiliation:
1 Little Wonga Rd, Cremorne, NSW 2090, Australia (email: donwb@iprimus.com.au)
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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.

Keywords

Leibniz algebrasLevi’s theorem

MSC classification

Secondary: 17A32: Leibniz algebras
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 86 , Issue 2 , October 2012 , pp. 184 - 185
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

References

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[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), 414–425.CrossRefGoogle Scholar
[4]Patsourakos, A., ‘On nilpotent properties of Leibniz algebras’, Comm. Algebra 35 (2007), 3828–3834.CrossRefGoogle Scholar