Automorphism Groups of nilpotent Lie algebras associated to certain graphs

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 ${\mathbb{Z}}_n$. Moreover, we prove that the (Lie) automorphism group of the corresponding nilpotent Lie algebra contains the dihedral group of order $2n$ as a subgroup.

References in corpus (3)

• Solvable Lie algebras and graphs
• Two-Step and Three-Step Nilpotent Lie Algebras Constructed from Schreier Graphs
• Geodesic orbit and naturally reductive nilmanifolds associated with graphs

Cited by in corpus (1)

• Abelian Factor in 2-step Nilpotent Lie Algebras Constructed from Graphs