MINIMAL NONNILPOTENT LEIBNIZ ALGEBRAS

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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