Quantum isometry group of dual of finitely generated discrete groups - II

Mandal, Arnab

Annales mathématiques Blaise Pascal, Tome 23 (2016) no. 2, pp. 219-247.

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 $C_r^{*}\left(\Gamma \right)$ 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 $\mathbb{Q}\left(\Gamma \right)$ turns out to be a doubling of $C^{*}\left(\Gamma \right)$.

Classification : 58B34, 46L87, 46L89
Mots clés : Compact quantum group, Quantum isometry group, Spectral triple

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