The Frucht property in the quantum group setting

Abstract

A classical theorem of Frucht states that any finite group appears as the automorphism group of a finite graph. In the quantum setting the problem is to understand the structure of the compact quantum groups which can appear as quantum automorphism groups of finite graphs. We discuss here this question, notably with a number of negative results.

arXiv comment41 pages; v3 further revisions, to appear in Glasg. Math. J

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• The hyperoctahedral quantum group
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Cited by in corpus (4)

• Classification of Quantum Graphs on $M_2$ and their Quantum Automorphism Groups
• Quantum symmetries of Cayley graphs of abelian groups
• Solution group representations as quantum symmetries of graphs
• Duals of finite quantum permutation groups