JournalsggdVol. 11, No. 2pp. 499–531

Full groups of Cuntz–Krieger algebras and Higman–Thompson groups

  • Kengo Matsumoto

    Joetsu University of Education, Japan
  • Hiroki Matui

    Chiba University, Japan
Full groups of Cuntz–Krieger algebras and Higman–Thompson groups cover
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Abstract

In this paper, we will study representations of the continuous full group ΓA\Gamma_A of a one-sided topological Markov shift (XA,σA)(X_A,\sigma_A) for an irreducible matrix AA with entries in {0,1}\{0,1\} as a generalization of Higman–Thompson groups VN,1<NNV_N, 1 < N \in {\mathbb{N}}. We will show that the group ΓA\Gamma_A can be represented as a group ΓAtab\Gamma_A^{\operatorname{tab}} of matrices, called AA-adic tables, with entries in admissible words of the shift space XAX_A, and a group ΓAPL\Gamma_A^{\operatorname{PL}} of right continuous piecewise linear functions, called AA-adic PL functions, on [0,1][0,1] with finite singularities.

Cite this article

Kengo Matsumoto, Hiroki Matui, Full groups of Cuntz–Krieger algebras and Higman–Thompson groups. Groups Geom. Dyn. 11 (2017), no. 2, pp. 499–531

DOI 10.4171/GGD/405