Second-Maximal Subalgebras of Leibniz Algebras
Lindsey Bosko-Dunbar, Jonathan Dunbar, J.T. Hird, Kristen Stagg
TL;DR
This paper classifies Leibniz algebras where second-maximal subalgebras are ideals, focusing on solvability, nilpotency, and derived algebra size, with specific descriptions over certain fields.
Contribution
It provides a detailed classification of Leibniz algebras with second-maximal subalgebras as ideals, including cases based on derived algebra codimension.
Findings
Classification of Leibniz algebras with second-maximal subalgebras as ideals
Descriptions of algebras with derived algebra of codimension zero or one
Identification of field-dependent algebra structures
Abstract
In this work we study Leibniz algebras whose second-maximal subalgebras are ideals. We provide a classification based on solvability, nilpotency, and the size of the derived algebra. We give specific descriptions of those Leibniz algebras whose derived algebra has codimension zero or one. This includes several algebras which are only possible over certain fields.
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Taxonomy
TopicsAdvanced Topics in Algebra · Rings, Modules, and Algebras · Algebraic structures and combinatorial models