Classical actions of quantum permutation groups

2023/06/30 by Freslon, Amaury, Taipe, Frank, Wang, Simeng
#FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2306.17502

Abstract

We describe explicitly all actions of the quantum permutation groups on classical compact spaces. In particular, we show that the defining action is the only non-trivial ergodic one. We then extend these results to all easy quantum groups associated to non-crossing partitions.

Related

• Embedding ergodic actions of compact quantum groups on C*-algebras into\n quotient spaces
• A state-space approach to quantum permutations
• Ergodic actions of the compact quantum group O_-1(2)
• Quantum symmetries of classical spaces
• Invariant subsets under compact quantum group actions