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• W2070147214 abstract "In order to begin an approach to the structure of arbitrary Leibniz algebras, (with no restrictions neither on the dimension nor on the base field), we introduce the class of split Leibniz algebras as the natural extension of the class of split Lie algebras. By developing techniques of connections of roots for this kind of algebras, we show that any of such algebras (L,[·,·]) is of the form L=U+∑jIj with U a subspace of the abelian subalgebra H, (in the sense [H,H]=0), and any Ij a well described ideal of L, satisfying [Ij,Ik]=0 if j≠k. In the case of L being of maximal length we characterize the simplicity of the algebra in terms of connections of roots." @default.
• W2070147214 created "2016-06-24" @default.
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• W2070147214 date "2012-03-01" @default.
• W2070147214 modified "2023-10-15" @default.
• W2070147214 title "On split Leibniz algebras" @default.
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• W2070147214 doi "https://doi.org/10.1016/j.laa.2011.02.046" @default.
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