Self-similar quantum groups

Nathan Brownlowe; David Robertson

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arXiv · 2302.01552

Self-similar quantum groups

Nathan Brownlowe·David Robertson

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Abstract

We introduce the notion of self-similarity for compact quantum groups. For a finite set $X$, we introduce a $C^*$-algebra $\mathbb{A}_X$, which is the quantum automorphism group of the infinite homogeneous rooted tree $X^*$. Self-similar quantum groups are then certain quantum subgroups of $\mathbb{A}_X$. 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.

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Nathan Brownlowe, David Robertson. 2023-02-03. Self-similar quantum groups. https://arxiv.org/abs/2302.01552

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