\({C}^{\ast}\)-algebras associated with lambda-synchronizing subshifts and flow equivalence (Q2873594)

The paper belongs to the cycle of the author's investigations of the interplay between the symbolic dynamics and structure of associated graph systems and \(C^*\)-algebras. It develops his recent work [\textit{W. Krieger} and \textit{K. Matsumoto}, Acta Appl. Math. 126, No. 1, 263--275 (2013; Zbl 1329.37010)] on \(\lambda\)-synchronizing subshifts \(\Lambda\). The latter class generalizing irreducible sofic shifts was introduced by Krieger and Matsumoto [loc. cit.]. Such \(\Lambda\) can be presented by a certain (\(\lambda\)-synchronizing \(\lambda\)-)graph system \(\lambda(\Lambda)\) determining the \(C^*\)-algebra \(\mathcal {O}_{\lambda(\Lambda)}\). Sufficient conditions for simplicity of this \(C^*\)-algebra are established. The stable isomorphism class of \(\mathcal {O}_{\lambda(\Lambda)}\) with its Cartan subalgebra proves to be a new invariant for flow equivalence of \(\lambda\)-synchronizing subshifts.