Self-similar quantum groups

2023/02/03 by Brownlowe, Nathan, Robertson, David · 1 citation
#FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2302.01552

Abstract

We introduce the notion of self-similarity for compact quantum groups. For a finite set X, we introduce a C^*-algebra \mathbbA_X, which is the quantum automorphism group of the infinite homogeneous rooted tree X^*. Self-similar quantum groups are then certain quantum subgroups of \mathbbA_X. Our main class of examples are called finitely-constrained self-similar quantum groups, and we find a class of these examples that can be described as quantum wreath products by subgroups of the quantum permutation group.

Cited by

• Tubular partitions and representations of the quantum automorphism group of a homogeneous rooted tree

Related

• Quantum permutation groups
• Discrete quantum subgroups of free unitary quantum groups
• Quantum automorphism groups and SO(3)-deformations
• On the structure of quantum automorphism groups
• On the similarity problem for locally compact quantum groups