Models of quantum permutations

Abstract

For N ≥ 4 we present a series of ∗-homomorphisms ϕn : C(S+ N ) → Bn where S+ N is the quantum permutation group. They are not necessarily representations of the quantum group S+ N but they yield good and somewhat “small” operator algebraic models of quantum permutation matrices. In the inverse limit however they produce a quantum group which turns out to be isomorphic to S+ N ; the latter fact is thanks to an argument by Alexandru Chirvasitu and Paweł Józiak building on topological generation.