Second-maximal subalgebras of Leibniz algebras

Lindsey Bosko-Dunbara Mathematics Discipline, St. Norbert College, De Pere, Wisconsin, USA

Jonathan D. Dunbara Mathematics Discipline, St. Norbert College, De Pere, Wisconsin, USA

J. T. Hirdb Department of Mathematics, West Virginia University, Institute of Technology, Montgomery, West Virginia, USACorrespondence[email protected]

Kristen Stagg Rovirac Department of Mathematics, California State University, Dominguez Hills, Carson, California, USA

Abstract

In this work we study Leibniz algebras whose second-maximal subalgebras are ideals. We provide classification based on solvability, nilpotency, and properties of the Frattini subalgebra. We give several specific descriptions of Leibniz algebras with these properties and include necessary and sufficient conditions for the non-nilpotent case.

KEYWORDS:

2020 Mathematics Subject Classification:

17A32

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Second-maximal subalgebras of Leibniz algebras

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Second-maximal subalgebras of Leibniz algebras

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