Nilpotent Lie and Leibniz algebras
Chelsie Batten Ray, Alexander Combs, Nicole Gin, Allison Hedges, J.T., Hird, Laurie Zack
TL;DR
This paper extends known results from finite-dimensional nilpotent Lie algebras to Leibniz algebras, providing new counterexamples and exploring one-generator cases in detail.
Contribution
It introduces new extensions of nilpotent Lie algebra results to Leibniz algebras and presents novel counterexamples, especially focusing on one-generator algebras.
Findings
Counterexamples to existing conjectures
Extension of nilpotent Lie algebra results to Leibniz algebras
Detailed analysis of one-generator Leibniz algebras
Abstract
We extend results on finite dimensional nilpotent Lie algebras to Leibniz algebras and counterexamples to others are found. One generator algebras are used in these examples and are investigated further.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Finite Group Theory Research