MINIMAL NONNILPOTENT LEIBNIZ ALGEBRAS

Year 2020, Volume: 28 Issue: 28, 187 - 192, 14.07.2020

Lindsey Bosko-dunbar Jonathan D. Dunbar J. T. Hırd Kristen Stagg Rovıra

https://doi.org/10.24330/ieja.768254

Cited By: 1

Abstract

We classify all nonnilpotent, solvable Leibniz algebras with the property that all proper subalgebras are nilpotent. This generalizes the work of [E. L. Stitzinger, Proc. Amer. Math. Soc., 28(1)(1971), 47-49] and [D. Towers, Linear Algebra Appl., 32(1980), 61-73] in Lie algebras. We show several examples which illustrate the differences between the Lie and Leibniz results. $~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$

Keywords

Nonnilpotent Leibniz algebra, solvable algebra, Lie algebra, maximal subalgebra, nilpotent subalgebra

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