Abelian subalgebras and ideals of maximal dimension in solvable Leibniz algebras

Ceballos, Manuel and Towers, David (2023) Abelian subalgebras and ideals of maximal dimension in solvable Leibniz algebras. Mediterranean Journal of Mathematics, 20 (2): 97. ISSN 1660-5446

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.