Fejér representations for discrete quantum groups and applications

2025/02/07 by Jason Crann, Crann, Jason, Kazemi, Soroush +2
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2502.05125

openalex publication_date 2025/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We prove that a discrete quantum group \mathbbG has the approximation property if and only if a Fejér-type representation holds for its C^*-algebraic or von Neumann algebraic crossed products. As applications, we extend several results from the literature to the context of discrete quantum groups with the approximation property. Additionally, we provide new characterizations of invariant L^∞(\widehat\mathbbG)-bimodules of B(ℓ²(\mathbbG)) and invariant C(\widehat\mathbbG)-bimodules of K(ℓ²(\mathbbG)), some of which are new in the group setting. Finally, we study Fubini crossed products of discrete quantum group actions.

Related

• Weak expectations of discrete quantum group algebras and crossed products
• Permanence of approximation properties for discrete quantum groups
• On the Baum--Connes conjecture for discrete quantum groups with torsion\n and the quantum Rosenberg Conjecture
• Residually finite quantum group algebras
• Amenable actions of discrete quantum groups on von Neumann algebras