Infinite quantum permutations
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 nonexistence of quantum symmetries in this setting.
 Publication:

arXiv eprints
 Pub Date:
 August 2022
 DOI:
 10.48550/arXiv.2208.01310
 arXiv:
 arXiv:2208.01310
 Bibcode:
 2022arXiv220801310V
 Keywords:

 Mathematics  Quantum Algebra;
 Mathematics  Operator Algebras;
 46L67;
 05C36;
 20B27;
 81P45
 EPrint:
 29 pages. Final version