ACTA issues

Simple $C^*$-algebras arising from certain Markov codes

Kengo Matsumoto

Acta Sci. Math. (Szeged) 80:1-2(2014), 95-120

Abstract. In this paper, we will study a certain Markov coded system $S_G$ defined by a finite directed graph $G$. We will prove that if the transition matrix of $G$ is aperiodic, the associated $C^*$-algebra ${\cal O}_{S_G}$ is unital, simple and purely infinite. We will compute its K-groups and Ext-groups and apply the results to classification of a certain class of symbolic dynamical systems under flow equivalence.

DOI: 10.14232/actasm-012-024-6

AMS Subject Classification (1991): 37B10; 46L35

Keyword(s): subshift, Markov code, $C^*$-algebra, K-theory, Bowen--Franks group, flow equivalence

Received April 12, 2012, and in final form January 16, 2014. (Registered under 24/2012.)