Automorphism Groups of nilpotent Lie algebras associated to certain graphs
Differential Geometry
2019-08-14 v2 Combinatorics
Rings and Algebras
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 . Moreover, we prove that the (Lie) automorphism group of the corresponding nilpotent Lie algebra contains the dihedral group of order as a subgroup.
Keywords
Cite
@article{arxiv.1812.09439,
title = {Automorphism Groups of nilpotent Lie algebras associated to certain graphs},
author = {Debraj Chakrabarti and Meera Mainkar and Savannah Swiatlowski},
journal= {arXiv preprint arXiv:1812.09439},
year = {2019}
}