Self-similar quantum groups

  • Nathan Brownlowe

    University of Sydney, Camperdown, Australia
  • David Robertson

    University of New England, Armidale, Australia
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Abstract

We introduce the notion of self-similarity for compact quantum groups. For a finite set , we introduce a -algebra , which is the quantum automorphism group of the infinite homogeneous rooted tree . Self-similar quantum groups are then certain quantum subgroups of . 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.

Cite this article

Nathan Brownlowe, David Robertson, Self-similar quantum groups. J. Noncommut. Geom. (2024), published online first

DOI 10.4171/JNCG/565