Uniform Lie Algebras and Uniformly Colored Graphs
Differential Geometry
2016-03-03 v1 Rings and Algebras
Abstract
Uniform Lie algebras are combinatorially defined two-step nilpotent Lie algebras which can be used to define Einstein solvmanifolds. These Einstein spaces often have nontrivial isotropy groups. We derive basic properties of uniform Lie algebras and we classify uniform Lie algebras with five or fewer generators. We define a type of directed colored graph called a uniformly colored graph and establish a correspondence between uniform Lie algebras and uniformly colored graphs. We present several methods of constructing infinite families of uniformly colored graphs and corresponding uniform Lie algebras.
Keywords
Cite
@article{arxiv.1603.00803,
title = {Uniform Lie Algebras and Uniformly Colored Graphs},
author = {Tracy L. Payne and Matthew Schroeder},
journal= {arXiv preprint arXiv:1603.00803},
year = {2016}
}