A Frattini Theory for Leibniz Algebras
Chelsie Batten, Lindsey Bosko-Dunbar, Allison Hedges, J. T. Hird,, Kristen Stagg, Ernest Stitzinger
TL;DR
This paper extends the Frattini theory, originally developed for Lie algebras, to Leibniz algebras, providing new insights into their structural properties.
Contribution
It introduces a Frattini theory for Leibniz algebras, expanding the existing Lie algebra results to a broader class of non-associative algebras.
Findings
Extended Frattini theory to Leibniz algebras
Established structural properties analogous to Lie algebras
Provided foundational results for further research
Abstract
A Frattini theory for non-associative algebras was developed by Towers and results for particular classes of algebras have appeared in various articles. Especially plentiful are results on Lie algebras. It is the purpose of this paper to extend some of the Lie algebra results to Leibniz algebras.
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Taxonomy
TopicsAdvanced Topics in Algebra · Rings, Modules, and Algebras · Algebraic structures and combinatorial models