Almost-reductive and almost-algebraic Leibniz algebra

Year 2024, Volume: 36 Issue: 36, 89 - 100, 12.07.2024

David A. Towers

https://doi.org/10.24330/ieja.1446322

Abstract

This paper examines whether the concept of an almost-algebraic Lie algebra developed by Auslander and Brezin in
[J. Algebra, 8(1968), 295-313] 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 between $\phi$-free, elementary, $E$-algebras and
$A$-algebras.

Keywords

Leibniz algebra, symmetric Leibniz algebra, Frattini ideal, $\phi$-free, elementary, $E$-algebra, $A$-algebra, almost-algebraic, almost-reductive

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