Geodesic
Full groups of Cuntz–Krieger algebras and Higman–Thompson groups
Kengo Matsumoto1 ; Hiroki Matui2
1Joetsu University of Education, Japan
2Chiba University, Japan
Groups, geometry, and dynamics, Tome 11 (2017) no. 2, pp. 499-531

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DOI

In this paper, we will study representations of the continuous full group ΓA​ of a one-sided topological Markov shift (XA​,σA​) for an irreducible matrix A with entries in {0,1} as a generalization of Higman–Thompson groups VN​,1<N∈N. We will show that the group ΓA​ can be represented as a group ΓAtab​ of matrices, called A-adic tables, with entries in admissible words of the shift space XA​, and a group ΓAPL​ of right continuous piecewise linear functions, called A-adic PL functions, on [0,1] with finite singularities.
DOI : 10.4171/ggd/405
Classification : 20-XX, 37-XX, 46-XX
Mots-clés : Higmann–Thompson group, Thompson group, Cuntz–Krieger algebra, topological Markov shift, full group

Kengo Matsumoto  1   ; Hiroki Matui  2

1 Joetsu University of Education, Japan
2 Chiba University, Japan 
Kengo Matsumoto; Hiroki Matui. Full groups of Cuntz–Krieger algebras and Higman–Thompson groups. Groups, geometry, and dynamics, Tome 11 (2017) no. 2, pp. 499-531. doi: 10.4171/ggd/405
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     author = {Kengo Matsumoto and Hiroki Matui},
     title = {Full groups of {Cuntz{\textendash}Krieger} algebras and {Higman{\textendash}Thompson} groups},
     journal = {Groups, geometry, and dynamics},
     pages = {499--531},
     year = {2017},
     volume = {11},
     number = {2},
     doi = {10.4171/ggd/405},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/405/}
}
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