Solvable Lie algebras and graphs

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.

minor changes

References in corpus (3)

• Two-Step and Three-Step Nilpotent Lie Algebras Constructed from Schreier Graphs
• Solsolitons associated with graphs
• Graphs and and two-step nilpotent Lie algebras

Cited by in corpus (3)

• Automorphism Groups of nilpotent Lie algebras associated to certain graphs
• On the cohomology of Lie algebras associated with graphs
• Abelian Factor in 2-step Nilpotent Lie Algebras Constructed from Graphs