Automorphism groups of nilpotent Lie algebras associated to certain graphs

Debraj Chakrabarti, Meera Mainkar, Savannah Swiatlowski

Research output: Contribution to journalArticlepeer-review

Abstract

We consider a family of 2-step nilpotent Lie algebras associated to uniform complete graphs on odd number of vertices. We prove that the symmetry group of such a graph is the holomorph of the additive cyclic group Zn Moreover, we prove that the (Lie) automorphism group of the corresponding nilpotent Lie algebra contains the dihedral group of order 2n as a subgroup.

Original languageEnglish
Pages (from-to)263-273
Number of pages11
JournalCommunications in Algebra
Volume48
Issue number1
DOIs
StatePublished - Jan 2 2020

Keywords

  • Automorphism group
  • edge-colored graphs
  • nilpotent Lie algebras

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