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Fall 2015 A note on reduced and von Neumann algebraic free wreath products
Jonas Wahl
Illinois J. Math. 59(3): 801-817 (Fall 2015). DOI: 10.1215/ijm/1475266409

Abstract

We study operator algebraic properties of the reduced and von Neumann algebraic versions of the free wreath products $\mathbb{G}\wr_{*}S_{N}^{+}$, where $\mathbb{G}$ is a compact matrix quantum group. Based on recent results on their corepresentation theory by Lemeux and Tarrago in [Lemeux and Tarrago (2014)], we prove that $\mathbb{G}\wr_{*}S_{N}^{+}$ is of Kac type whenever $\mathbb{G}$ is, and that the reduced version of $\mathbb{G}\wr_{*}S_{N}^{+}$ is simple with unique trace state whenever $N\geq8$. Moreover, we prove that the reduced von Neumann algebra of $\mathbb{G}\wr_{*}S_{N}^{+}$ does not have property $\Gamma$.

Citation

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Jonas Wahl. "A note on reduced and von Neumann algebraic free wreath products." Illinois J. Math. 59 (3) 801 - 817, Fall 2015. https://doi.org/10.1215/ijm/1475266409

Information

Received: 11 February 2016; Revised: 22 March 2016; Published: Fall 2015
First available in Project Euclid: 30 September 2016

zbMATH: 1355.46056
MathSciNet: MR3554234
Digital Object Identifier: 10.1215/ijm/1475266409

Subjects:
Primary: 46L54

Rights: Copyright © 2015 University of Illinois at Urbana-Champaign

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Vol.59 • No. 3 • Fall 2015
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