Title of article :
MINIMAL NONNILPOTENT LEIBNIZ ALGEBRAS
Author/Authors :
Bosko-Dunbar, Lindsey Mathematics Discipline St - Norbert College , Dunbar, Jonathan D. Mathematics Discipline St - Norbert College , Hird, J.T. Department of Mathematics - West Virginia University - Institute of Technology Beckley , Stagg Rovira, Kristen Department of Mathematics - California State University - Dominguez Hills Carson
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
Journal title :
International Electronic Journal of Algebra
