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Blaise Pascal
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Arnab Mandal
Quantum isometry group of dual of finitely generated discrete groups - II
Annales mathématiques Blaise Pascal, 23 no. 2 (2016), p. 219-247, doi: 10.5802/ambp.361
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Class. Math.: 58B34, 46L87, 46L89
Mots clés: Compact quantum group, Quantum isometry group, Spectral triple

Résumé - Abstract

As a continuation of the programme of [13], we carry out explicit computations of $\mathbb{Q}(\Gamma ,S)$, the quantum isometry group of the canonical spectral triple on $C_{r}^{*}(\Gamma )$ coming from the word length function corresponding to a finite generating set S, for several interesting examples of $\Gamma $ not covered by the previous work [13]. These include the braid group of 3 generators, $\mathbb{Z}_4^{*n}$ etc. Moreover, we give an alternative description of the quantum groups $H_s^{+}(n,0)$ and $K_n^{+}$ (studied in [3], [4]) in terms of free wreath product. In the last section we give several new examples of groups for which $\mathbb{Q}(\Gamma )$ turns out to be a doubling of $C^*(\Gamma )$.

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