Frattini Properties and Nilpotency in Leibniz Algebras
Allison McAlister, Kristen Stagg Rovira, and Ernie Stitzinger
TL;DR
This paper explores ideals with Frattini-like properties in Leibniz algebras, extending concepts from group theory and Lie algebras, with a focus on nilpotency and new theoretical results.
Contribution
It introduces new properties of ideals in Leibniz algebras related to the Frattini ideal and investigates their implications for nilpotency.
Findings
New properties of ideals in Leibniz algebras related to Frattini ideals
Results connecting these properties to nilpotency in Leibniz algebras
Most findings are novel even for Lie algebras
Abstract
Ideals that share properties with the Frattini ideal of a Leibniz algebra are studied. Similar investigations have been considered in group theory. However most of the results are new for Lie algebras. Many of the results involve nilpotency of these algebras.
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