Almost-reductive and almost-algebraic Leibniz algebra

Authors : David A Towers

Pages : 89-100

Doi:10.24330/ieja.1446322

View : 69 | Download : 76

Publication Date : 2024-07-12

Article Type : Research Paper

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