arXiv subjects
Publications and source records attributed to Allison McAlister.
In extending results from Lie to Leibniz algebras, it is helpful to have techniques which translate results from the former to the latter without having to repeat the (perhaps modified) arguments. Such a technique is developed in this work, and some applications are given.
Ideals that share properties with the Frattini ideal of a Leibniz algebra are studied. Similar investigations have been considered in group theory. However most of the results are new for Lie algebras. Many of the results involve nilpotency of these algebras.
We show that for fields that are of characteristic 0 or algebraically closed of characteristic greater than 5, that certain classes of Leibniz algebras are 2-recognizeable. These classes are solvable, strongly solvable and super solvable. These results hold in Lie algebras and in general for groups.
We develop Jacobson's refinement of Engel's Theorem for Leibniz algebras. We then note some consequences of the result.