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.

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

References in corpus (2)

• Study of quantum symmetries for vertex-transitive graphs using intertwiner spaces
• Existence of quantum symmetries for graphs on up to seven vertices: a computer based approach

Cited by in corpus (1)

• Duals of finite quantum permutation groups