Journal of Operator Theory

Volume 94, Issue 2, Autumn 2025 pp. 527-558.

Classical actions of quantum permutation groups

Authors: Amaury Freslon (1), Frank Taipe (2), Simeng Wang (3)
Author institution: (1) Laboratoire de Mathematiques d'Orsay, CNRS, Universite Paris-Saclay, 91405 Orsay, France
(2) Instituto de Matematica y Ciencias Afines, Universidad Nacional de Ingenieria, Lima 15012, Peru
(3) Institute for Advanced Study in Mathematics, Harbin Institute of Technology, Harbin 150001, China

Summary: We present a complete study of rigidity for actions of quantum permutation groups on compact spaces. In particular, we describe explicitly all actions of the quantum permutation groups on classical compact spaces, and show that the defining action is the only non-trivial ergodic one. We then extend these results to all easy quantum groups associated with non-crossing partitions.

DOI: http://dx.doi.org/10.7900/jot.2024feb16.2464
Keywords: quantum permutation groups, actions, non-crossing partitions, easy quantum groups

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