2019
DOI: 10.1080/00927872.2019.1640239
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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 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.

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