Leibniz algebras with an abelian subalgebra of codimension tw0

2024/07/16 by Amir Fernández Ouaridi, Ouaridi, A. Fernandez, David A. Towers +1
Mathematics · Materials Science · #Advanced Topics in Algebra #Advanced Differential Equations and Dynamical Systems #Liquid Crystal Research Advancements

paper · pdf · doi:10.48550/arxiv.2407.11757

Abstract

A characterization of the finite-dimensional Leibniz algebras with an abelian subalgebra of codimension two over a field \mathbbF of characteristic p≠2 is given. In short, a finite-dimensional Leibniz algebra of dimension n with an abelian subalgebra of codimension two is solvable and contains an abelian ideal of codimension at most two or it is a direct sum of a Lie one-dimensional solvable extension of the Heisenberg algebra \mathfrakh(\mathbbF) and \mathbbF^n-4 or a direct sum of a 3-dimensional simple Lie algebra and \mathbbF^n-3 or a Leibniz one-dimensional solvable extension of the algebra \mathfrakh(\mathbbF) ⊕ \mathbbF^n-4.

Related

• Abelian subalgebras and ideals of maximal dimension in Leibniz algebras
• Engel subalgebras of Leibniz algebras
• Modularity conditions in Leibniz algebras
• Second-Maximal Subalgebras of Leibniz Algebras
• Leibniz A-algebras