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

2014/09/17 by Kengo Matsumoto, Matsumoto, Kengo, Hiroki Matui +1
Mathematics · #37A55 #37B10 #46L35 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR) #Operator Algebras (math.OA) #Primary 20F38 #Secondary 20F65 #math.DS #math.GR #math.OA #msc:20F38 #msc:20F65 #msc:37A55 #msc:37B10 #msc:46L35

paper · pdf · doi:10.48550/arxiv.1409.4838

27 pages, This is a final version to appear in "Groups, Geometry, and Dynamics"

openalex publication_date 2014/09/17 · arxiv created 2016/10/04 · arxiv updated 2016/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we will study presentations of the continuous full group Γ_A of a one-sided topological Markov shift (X_A,σ_A) for an irreducible matrix A with entries in \0,1\ as a generalization of Higman-Thompson groups V_N, 1<N ∈ ℕ. We will show that the group Γ_A can be represented as a group Γ_A^tab of matrices, called A-adic tables, with entries in admissible words of the shift space X_A, and a group Γ_A^PL of right continuous piecewise linear functions, called A-adic PL functions, on [0,1] with finite singularities.

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