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Keywords:
Lie algebras; Leibniz algebras; $A$-algebras; Frattini ideal; solvable; nilpotent; completely solvable; metabelian; monolithic; cyclic Leibniz algebras
Lie algebras; Leibniz algebras; $A$-algebras; Frattini ideal; solvable; nilpotent; completely solvable; metabelian; monolithic; cyclic Leibniz algebras
Summary:
A finite-dimensional Lie algebra is called an $A$-algebra if all of its nilpotent subalgebras are abelian. These arise in the study of constant Yang-Mills potentials and have also been particularly important in relation to the problem of describing residually finite varieties. They have been studied by several authors, including Bakhturin, Dallmer, Drensky, Sheina, Premet, Semenov, Towers and Varea. In this paper we establish generalisations of many of these results to Leibniz algebras.
References:
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