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arXiv · 2105.06797

Abelian subalgebras and ideals of maximal dimension in Leibniz algebras

Manuel Ceballos·David A. Towers
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Abstract

In this paper, we compare the abelian subalgebras and ideals of maximal dimension for finite-dimensional Leibniz algebras. We study Leibniz algebras containing abelian subalgebras of codimension 1, solvable and supersolvable Leibniz algebras for codimensions 1 and 2, nilpotent Leibniz algebras in case of codimension 2 and we also analyze the case of k-abelian p-filiform Leibniz algebras. Throughout the paper, we also give examples to clarify some results and the need for restrictions on the underlying field.

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Manuel Ceballos, David A. Towers. 2021-05-14. Abelian subalgebras and ideals of maximal dimension in Leibniz algebras. https://arxiv.org/abs/2105.06797

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