MINIMAL NONNILPOTENT LEIBNIZ ALGEBRAS

Authors : Lindsey BOSKODUNBAR, Jonathan D DUNBAR, J T HIRD, Kristen Stagg ROVIRA

Pages : 187-192

Doi:10.24330/ieja.768254

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Publication Date : 2020-07-14

Article Type : Research Paper

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., 28insert ignore into journalissuearticles values(1);insert ignore into journalissuearticles values(1971);, 47-49] and [D. Towers, Linear Algebra Appl., 32insert ignore into journalissuearticles values(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