Almost reductive and almost algebraic Leibniz algebras

Towers, David (2024) Almost reductive and almost algebraic Leibniz algebras. International Electronic Journal of Algebra, 36 (36): 7. pp. 89-100.

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Abstract

This paper examines whether the concept of an almost-algebraic Lie algebra developed by Auslander and Brezin can be introduced for Leibniz algebras. Two possible analogues are considered: almost-reductive and almost-algebraic Leibniz algebras. For Lie algebras these two concepts are the same, but that is not the case for Leibniz algebras, the class of almost-algebraic Leibniz algebras strictly containing that of the almost-reductive ones. Various properties of these two classes of algebras are obtained, together with some relationships to $\phi$-free, elementary, $E$-algebras and $A$-algebras.