# American Institute of Mathematical Sciences

August  2013, 33(8): 3753-3765. doi: 10.3934/dcds.2013.33.3753

## K-groups of the full group actions on one-sided topological Markov shifts

 1 Department of Mathematics, Joetsu University of Education, Joetsu 943-8512, Japan

Received  May 2012 Revised  July 2012 Published  January 2013

Let $(X_A,\sigma_A)$ be the one-sided topological Markov shift for an $N\times N$ irreducible matrix $A$ with entries in $\{ 0,1 \}$. We will first show that the continuous full group $\Gamma_A$ of $(X_A,\sigma_A)$ is non amenable as a discrete group and contains all finite groups and free groups. We will second introduce the K-group $K^0(X_A,\Gamma_A)$ for the action of $\Gamma_A$ on $X_A$, and show that the group $K^0(X_A,\Gamma_A)$ with the position of the constant $1$ function is a complete invariant for the topological conjugacy class of the action of $\Gamma_A$ on $X_A$ under some conditions.
Citation: Kengo Matsumoto. K-groups of the full group actions on one-sided topological Markov shifts. Discrete & Continuous Dynamical Systems, 2013, 33 (8) : 3753-3765. doi: 10.3934/dcds.2013.33.3753
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