Frattini Properties and Nilpotency in Leibniz Algebras

McAlister, Allison; Rovira, Kristen Stagg; Stitzinger, Ernest L.

doi:10.48550/arxiv.1506.04996

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2016

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“…Much of the recent work in Leibniz algebras has focused on classifying Leibniz algebras based on either their dimension [1,6,13], their nilradical [5,7,8], or their maximal and Frattini subalgebras [3,12]. The present body of work falls into this last category.…”

Section: Introductionmentioning

confidence: 99%

Second-Maximal Subalgebras of Leibniz Algebras

Bosko-Dunbar¹,

Dunbar²,

Stagg³

2016

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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.2010 Mathematics Subject Classification. 17D99.

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