The free wreath product of a discrete group by a quantum automorphism group
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- by Lorenzo Pittau PDF
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Abstract:
Let $\mathbb {G}$ be the quantum automorphism group of a finite dimensional C*-algebra $(B,\psi )$ and $\Gamma$ a discrete group. We want to compute the fusion rules of $\widehat {\Gamma }\wr _* \mathbb {G}$. First of all, we will revise the representation theory of $\mathbb {G}$ and, in particular, we will describe the spaces of intertwiners by using noncrossing partitions. It will allow us to find the fusion rules of the free wreath product in the general case of a state $\psi$. We will also prove the simplicity of the reduced C*-algebra, when $\psi$ is a trace, as well as the Haagerup property of $L^\infty (\widehat {\Gamma }\wr _* \mathbb {G})$, when $\Gamma$ is moreover finite.References
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Additional Information
- Lorenzo Pittau
- Affiliation: Université de Cergy-Pontoise, 95000, Cergy-Pontoise, France — and — Univ. Paris Diderot, Sorbonne Paris Cité, IMJ-PRG, UMR 7586 CNRS, Sorbonne Universités, UPMC Univ Paris 06, F-75013, Paris, France
- Email: lorenzo.pittau@u-cergy.fr
- Received by editor(s): October 6, 2014
- Received by editor(s) in revised form: May 14, 2015
- Published electronically: January 27, 2016
- Communicated by: Ken Ono
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 1985-2001
- MSC (2010): Primary 46L65, 81R50
- DOI: https://doi.org/10.1090/proc/12975
- MathSciNet review: 3460161