Modularity conditions in Leibniz algebras

Paez-Guillan, Pilar and Siciliano, Salvatore and Towers, David (2024) Modularity conditions in Leibniz algebras. Journal of Algebra and Its Applications. ISSN 0219-4988

Text (paez-siciliano-towers_modularLeibniz_final1(1)) - Accepted Version
Available under License Creative Commons Attribution.
Download (0B)

Text (paez-siciliano-towers_modularLeibniz_final1(1))
paez_siciliano_towers_modularLeibniz_final1_1_.pdf - Accepted Version
Available under License Creative Commons Attribution.
Download (283kB)

Abstract

In this paper we continue the study of the subalgebra lattice of a Leibniz algebra. In particular, we find out that solvable Leibniz algebras with an upper semi-modular lattice are either almost-abelian or have an abelian ideal spanned by the elements with square zero. We also study Leibniz algebras in which every subalgebra is a weak quasi-ideal, as well as modular symmetric Leibniz algebras.