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    Ceballos, Manuel Núñez, Juan and Tenorio, Ángel F. 2015. Algorithmic procedure to compute abelian subalgebras and ideals of maximal dimension of Leibniz algebras. International Journal of Computer Mathematics, Vol. 92, Issue. 9, p. 1838.


    Fialowski, A. and Mihálka, É. Zs. 2015. Representations of Leibniz Algebras. Algebras and Representation Theory, Vol. 18, Issue. 2, p. 477.


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    Militaru, G. 2015. The global extension problem, co-flag and metabelian Leibniz algebras. Linear and Multilinear Algebra, Vol. 63, Issue. 3, p. 601.


    Rakhimov, I. S. Masutova, K. K. and Omirov, B. A. 2015. On Derivations of Semisimple Leibniz Algebras. Bulletin of the Malaysian Mathematical Sciences Society,


    Batten Ray, Chelsie Hedges, Allison and Stitzinger, Ernest 2014. Classifying Several Classes of Leibniz Algebras. Algebras and Representation Theory, Vol. 17, Issue. 2, p. 703.


    Camacho, L.M. Cañete, E.M. Gómez, J.R. and Omirov, B.A. 2014. p-Filiform Leibniz algebras of maximum length. Linear Algebra and its Applications, Vol. 450, p. 316.


    Khudoyberdiyev, A.Kh. Rakhimov, I.S. and Said Husain, Sh.K. 2014. On classification of 5-dimensional solvable Leibniz algebras. Linear Algebra and its Applications, Vol. 457, p. 428.


    Khudoyberdiyev, A.Kh. Ladra, M. and Omirov, B.A. 2014. On solvable Leibniz algebras whose nilradical is a direct sum of null-filiform algebras. Linear and Multilinear Algebra, Vol. 62, Issue. 9, p. 1220.


    Agore, A.L. and Militaru, G. 2013. Unified products for Leibniz algebras. Applications. Linear Algebra and its Applications, Vol. 439, Issue. 9, p. 2609.


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  • Bulletin of the Australian Mathematical Society, Volume 86, Issue 2
  • October 2012, pp. 184-185

ON LEVI’S THEOREM FOR LEIBNIZ ALGEBRAS

  • DONALD W. BARNES (a1)
  • DOI: http://dx.doi.org/10.1017/S0004972711002954
  • Published online: 30 November 2011
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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