Classifying Several Classes of Leibniz Algebras

Abstract

We extend results related to maximal subalgebras and ideals from Lie to Leibniz algebras. In particular, we classify minimal non-elementary Leibniz algebras and Leibniz algebras with a unique maximal ideal. In both cases, there are types of these algebras with no Lie algebra analogue. We also give a classification of E-Leibniz algebras which is very similiar to its Lie algebra counterpart. Note that a classification of elementary Leibniz algebras has been shown in [3].

Solvable Leibniz Algebras with Heisenberg Nilradical

“…In particular, there has been interest in extending classifications of certain classes of Lie algebras to classifications of corresponding Leibniz algebras [2,4,5,8,9,11].…”

“…In particular, there has been interest in extending classifications of certain classes of Lie algebras to classifications of corresponding Leibniz algebras [2,4,5,8,9,11]. Some of the classifications of Lie algebras come from placing certain restrictions on the nilradical [7,15,17,18].…”