Haagerup property for quantum reflection groups

2013/03/09 by François Lemeux, Lemeux, François
Mathematics · #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA) #math.OA #math.QA

paper · pdf · doi:10.48550/arxiv.1303.2151

15 pages, minor corrections

arxiv created 2013/09/05 · arxiv updated 2013/09/06

Abstract

In this paper we prove that the duals of the quantum reflection groups have the Haagerup property for all N≥4 and s∈[1,∞). We use the canonical arrow onto the quantum permutation groups, and we describe how the characters of the quantum reflection groups behave with respect to this canonical morphism thanks to the description of the fusion rules binding irreducible corepresentations of H_N^s+. This allows us to construct states on the central algebra of H_N^s+ and to use a fundamental theorem proved by M.Brannan giving a method to construct nets of trace-preserving, normal, unital and completely positive maps on the von Neumann algebra of a compact quantum group of Kac type.

Related

• Haagerup approximation property via bimodules
• Topological generation and matrix models for quantum reflection groups
• The Haagerup property for arbitrary von Neumann algebras
• Quantum permutation groups
• Property T for general locally compact quantum groups