Infinite quantum permutations

Voigt, C. (2023) Infinite quantum permutations. Advances in Mathematics, 415, 108887. (doi: 10.1016/j.aim.2023.108887)

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We define and study quantum permutations of infinite sets. This leads to discrete quantum groups which can be viewed as infinite variants of the quantum permutation groups introduced by Wang. More precisely, the resulting quantum groups encode universal quantum symmetries of the underlying sets among all discrete quantum groups. We also discuss quantum automorphisms of infinite graphs, including some examples and open problems regarding both the existence and non-existence of quantum symmetries in this setting.

Item Type:Articles
Additional Information:This work was supported by EPSRC grant EP/T03064X/1.
Glasgow Author(s) Enlighten ID:Voigt, Professor Christian
Authors: Voigt, C.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Advances in Mathematics
ISSN (Online):1090-2082
Published Online:02 February 2023
Copyright Holders:Copyright © 2023 The Authors
First Published:First published in Advances in Mathematics 415:108887
Publisher Policy:Reproduced under a Creative Commons License

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
309470Quantum groups in actionChristian VoigtEngineering and Physical Sciences Research Council (EPSRC)EP/T03064X/1M&S - Mathematics