arXiv subjects

S. McKay Sullivan

Publications and source records attributed to S. McKay Sullivan.

3 recordsLinked to original sources

arXiv2014

Classification of Complex Cyclic Leibniz Algebras

Since Leibniz algebras were introduced by Loday as a generalization of Lie algebras, there has been a lot of interest in which results of the latter extend to the former. Cyclic algebras, those generated by one element, are a useful tool for studying these concepts. In fact, they have no Lie algebra counterpart. Their simple structure lends itself to elegant counterexamples to the extension of several important results from Lie algebras to Leibniz algebras. In this paper, we give a classification of cyclic Leibniz algebras.

math.RA↗

arXiv2014

2-Recognizeable Classes of Leibniz 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.

math.RA↗

arXiv2014

Cyclic Leibniz Algebras

Leibniz algebras generated by one element, called cyclic, provide simple and illuminating examples of many basic concepts. It is the purpose of this paper to illustrate this fact.

math.RA↗