Quantum isometry group of dual of finitely generated discrete groups- \textrmII

2015/04/09 by Arnab Mandal, Mandal, Arnab
Mathematics · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1504.02240

openalex publication_date 2015/04/09 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

As a contribution of the programme of Goswami and Mandal (2014), 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 Goswami and Mandal (2014). These include the braid group of 3 generators, ℤ₄^*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 ℚ(Γ) turn out to be doubling of C^*(Γ).

Citations

• Notes on Compact Quantum Groups

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