Abelian factors in 2-step nilpotent Lie algebras constructed from graphs

Rachelle DeCoste, Lisa DeMeyer, Meera Mainkar, Allie Ray

Research output: Contribution to journalArticlepeer-review


We consider real 2-step metric nilpotent Lie algebras associated to graphs with possibly repeated edge labels as constructed by Ray in 2016. We determine how the structure of the edge labeling within the graph contributes to the abelian factor in these Lie algebras. Furthermore, we explicitly compute the abelian factor of the 2-step nilpotent Lie algebras associated with some families of graphs such as star graphs, cycles, Schreier graphs, and properly edge-colored graphs. We also study the singularity properties of these Lie algebras in certain cases.

Original languageEnglish
Pages (from-to)2155-2175
Number of pages21
JournalCommunications in Algebra
Issue number5
StatePublished - 2023


  • Abelian factor
  • edge-labeled graph
  • nilpotent Lie algebra


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