Frucht's theorem for finite quantum groups
Organizers
Speaker
Mateusz Wasilewski
Time
Wednesday, April 9, 2025 3:00 PM - 4:30 PM
Venue
A3-2-201
Online
Zoom 928 682 9093
(BIMSA)
Abstract
A classical result of Frucht says that every finite group can be realized as an automorphism group of a finite graph. Due to Banica and McCarthy, the following analogue does not hold: not every finite quantum group is the quantum automorphism group of a finite graph, e.g. the dual of the permutation group on three generators. Nevertheless we obtained a version of Frucht's theorem utilizing quantum graphs: every finite quantum group is the quantum automorphism group of a finite quantum graph. Moreover, the argument is more efficient than the original one in the case of classical groups. For a given finite quantum group we also tackled the following question: when can we find a quantum Cayley graph, whose quantum automorphism group is the original finite quantum group. I will offer some answers, mostly for duals of classical groups.
Reference: https://arxiv.org/abs/2503.11149 (by Michael Brannan, Daniel Gromada, Junichiro Matsuda, Adam Skalski, Mateusz Wasilewski)
Reference: https://arxiv.org/abs/2503.11149 (by Michael Brannan, Daniel Gromada, Junichiro Matsuda, Adam Skalski, Mateusz Wasilewski)
Speaker Intro
He is an assistant professor at the Institute of Mathematics of the Polish Academy of Sciences. He is interested in quantum graphs, quantum groups, von Neumann algebras, and abstract harmonic analysis.