Self-similar quantum groups

Abstract: Quantum automorphism groups originated in the work of Wang in the mid 90s as an answer to question of Connes: what are the quantum automorphisms of a space? Wang showed that for a finite set with at least 4 points there are an infinite number of quantum permutations. Since then, work on quantum automorphism groups has progressed in many different directions, including the construction of the quantum automorphism group of a finite graph by Bichon in 2004 and quantum automorphisms of locally finite graphs by Rollier and Vaes in 2022. In a recent preprint with Nathan Brownlowe, we have shown that the quantum automorphism group of a homogeneous rooted tree is a compact quantum group, and defined when a quantum subgroup is self-similar. In this talk I will give an overview of this construction, and construct a number of examples through an analogue of the notion of a finitely constrained self-similar group defined by Sunic in 2011.

group theory

Audience: researchers in the discipline

Symmetry in Newcastle