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Abelian subalgebras and ideals of maximal dimension in solvable Leibniz algebras

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Published
Article number97
<mark>Journal publication date</mark>3/02/2023
<mark>Journal</mark>Mediterranean Journal of Mathematics
Issue number2
Volume20
Number of pages23
Publication StatusPublished
<mark>Original language</mark>English

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.