Infinite quantum permutations
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Publication:6406722
DOI10.1016/J.AIM.2023.108887arXiv2208.01310MaRDI QIDQ6406722
Publication date: 2 August 2022
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.
Permutations, words, matrices (05A05) Infinite automorphism groups (20B27) Quantum information, communication, networks (quantum-theoretic aspects) (81P45) Quantum groups (operator algebraic aspects) (46L67)
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