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

Arnab Mandal

doi:10.5802/ambp.361

Arnab Mandal ¹

¹ Indian Statistical Institute 203, B. T Road Kolkata 700108, India

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

Résumé

As a continuation of the programme of [13], we carry out explicit computations of $ℚ (Γ, S)$ , the quantum isometry group of the canonical spectral triple on $C_{r}^{*} (Γ)$ coming from the word length function corresponding to a finite generating set S, for several interesting examples of $Γ$ not covered by the previous work [13]. These include the braid group of 3 generators, $ℤ_{4}^{* n}$ 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 $ℚ (Γ)$ turns out to be a doubling of $C^{*} (Γ)$ .

DOI : 10.5802/ambp.361

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

Affiliations des auteurs :

Arnab Mandal ¹

¹ Indian Statistical Institute 203, B. T Road Kolkata 700108, India

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Arnab Mandal. Quantum isometry group of dual of finitely generated discrete groups - II. Annales mathématiques Blaise Pascal, Tome 23 (2016) no. 2, pp. 219-247. doi : 10.5802/ambp.361. https://ambp.centre-mersenne.org/articles/10.5802/ambp.361/

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