Solvable Lie algebras and graphs
Rings and Algebras
2017-09-21 v2 Combinatorics
Differential Geometry
Abstract
We define a solvable extension of the graph 2-step nilpotent Lie algebras of [5] by adding elements corresponding to the 3-cliques of the graph. We study some of their basic properties and we prove that two such Lie algebras are isomorphic if and only if their graphs are isomorphic. We also briefly discuss some metric properties, providing examples of homogeneous spaces with nonpositive curvature operator and solvsolitons.
Cite
@article{arxiv.1604.07856,
title = {Solvable Lie algebras and graphs},
author = {Gueo Grantcharov and Vladimir Grantcharov and Plamen Iliev},
journal= {arXiv preprint arXiv:1604.07856},
year = {2017}
}
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