Self-similar quantum groups

Nathan Brownlowe; David Robertson

doi:10.4171/jncg/565

Self-similar quantum groups

Nathan Brownlowe
, David Robertson

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We introduce the notion of self-similarity for compact quantum groups. For a finite set X, we introduce a C* -algebra 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 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.

Original language	English
Pages (from-to)	1-25
Journal	Journal of Noncommutative Geometry
DOIs	https://doi.org/10.4171/jncg/565
Publication status	Published - 2 Apr 2024

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https://hdl.handle.net/1959.11/61675

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title = "Self-similar quantum groups",

abstract = "We introduce the notion of self-similarity for compact quantum groups. For a finite set X, we introduce a C* -algebra AX, which is the quantum automorphism group of the infinite homogeneous rooted tree X*. Self-similar quantum groups are then certain quantum subgroups of AX. 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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AB - We introduce the notion of self-similarity for compact quantum groups. For a finite set X, we introduce a C* -algebra AX, which is the quantum automorphism group of the infinite homogeneous rooted tree X*. Self-similar quantum groups are then certain quantum subgroups of AX. 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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JO - Journal of Noncommutative Geometry

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Self-similar quantum groups

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