2023/09/07 by Towers, David A.
#17B05 #17B20 #17B30 #17B50 #FOS: Mathematics #Group Theory (math.GR) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2309.03680
This paper examines whether the concept of an almost-algebraic Lie algebra developed by Auslander and Brezin in \citeab 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 ϕ-free, elementary, E-algebras and A-algebras.