Quantum isometry group of dual of finitely generated discrete groups- $\text{II}$

Abstract

As a contribution of the programme of Goswami and Mandal (2014), we carry out explicit computations of $\mathbb{Q}(\Gamma ,S)$, the quantum isometry group of the canonical spectral triple on $C_r^{\ast }(\Gamma )$ 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 Goswami and Mandal (2014). These include the braid group of 3 generators, ${\mathbb{Z}}_4^{\ast n}$ etc. Moreover, we give an alternative description of the quantum groups $H_s^{+}(n,0)$ and $K_n^{+}$ (studied in Banica and Skalski (2012), Banica and Skalski (2013)) in terms of free wreath product. In the last section we give several new examples of groups for which $\mathbb{Q}(\Gamma )$ turn out to be doubling of $C^{\ast }(\Gamma )$.

To appear in Annales Mathematiques Blaise Pascal. arXiv admin note: text overlap with arXiv:1309.1294 by other authors

References in corpus (1)

• Existence and examples of quantum isometry group for a class of compact metric spaces