Infinite quantum permutations

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

Abstract

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.
• Status: Published
• Refereed: Yes
• 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
• Publisher: Elsevier
• ISSN: 0001-8708
• 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

Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
309470		Quantum groups in action	Christian Voigt	Engineering and Physical Sciences Research Council (EPSRC)	EP/T03064X/1	M&S - Mathematics