Topological generation and matrix models for quantum reflection groups

2018/08/26 by Brannan, Michael, Chirvasitu, Alexandru, Freslon, Amaury
#FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1808.08611

Abstract

We establish several new topological generation results for the quantum permutation groups S⁺_N and the quantum reflection groups H^s+_N. We use these results to show that these quantum groups admit sufficiently many "matrix models". In particular, all of these quantum groups have residually finite discrete duals (and are, in particular, hyperlinear), and certain "flat" matrix models for S_N⁺ are inner faithful.

Related

• Quantum permutation groups
• Models of quantum permutations
• Haagerup property for quantum reflection groups
• Modelling questions for transitive quantum groups
• A Connection between Easy Quantum Groups, Varieties of Groups and Reflection Groups