On Levi-Malcev theorem for Leibniz algebras

30 Oct 2017 · Kudaybergenov Karimbergen, Ladra Manuel, Omirov Bakhrom ·

The present paper is devoted to provide conditions for the Levi--Malcev theorem to hold or not to hold (i.e. for two Levi subalgebras to be or not conjugate by an inner automorphism) in the context of finite-dimensional Leibniz algebras over a field of characteristic zero. Particularly, in the case of the field $\mathbb{C}$ of complex numbers, we consider all possible cases in which Levi subalgebras are conjugate and not conjugate.

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On Levi-Malcev theorem for Leibniz algebras

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