Fejér representations for discrete quantum groups and applications

Fuente: arXiv
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Main Authors: Crann, Jason, Kazemi, Soroush, Neufang, Matthias
Format: Preprint
Published: 2025
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author Crann, Jason
Kazemi, Soroush
Neufang, Matthias
author_facet Crann, Jason
Kazemi, Soroush
Neufang, Matthias
contents We prove that a discrete quantum group $\mathbb{G}$ 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 $L^\infty(\widehat{\mathbb{G}})$-bimodules of $\mathcal{B}(\ell^2(\mathbb{G}))$ and invariant $C(\widehat{\mathbb{G}})$-bimodules of $\mathcal{K}(\ell^2(\mathbb{G}))$, some of which are new in the group setting. Finally, we study Fubini crossed products of discrete quantum group actions.
format Preprint
id arxiv_https___arxiv_org_abs_2502_05125
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Fejér representations for discrete quantum groups and applications
Crann, Jason
Kazemi, Soroush
Neufang, Matthias
Operator Algebras
Functional Analysis
We prove that a discrete quantum group $\mathbb{G}$ 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 $L^\infty(\widehat{\mathbb{G}})$-bimodules of $\mathcal{B}(\ell^2(\mathbb{G}))$ and invariant $C(\widehat{\mathbb{G}})$-bimodules of $\mathcal{K}(\ell^2(\mathbb{G}))$, some of which are new in the group setting. Finally, we study Fubini crossed products of discrete quantum group actions.
title Fejér representations for discrete quantum groups and applications
topic Operator Algebras
Functional Analysis
url https://arxiv.org/abs/2502.05125