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

Abstract

A certain synchronizing property for subshifts called $\lambda$-synchronization yields $\lambda$-graph systems called the $\lambda$-synchronizing $\lambda$-graph systems for the subshifts. The $\lambda$-synchronizing $\lambda$-graph system is a left Fischer cover analogue for a $\lambda$-synchronizing subshift. We will study algebraic structure of the $C^{\ast }$-algebra associated with the $\lambda$-synchronizing $\lambda$-graph system and prove that the stable isomorphism class of the $C^{\ast }$-algebra with its Cartan subalgebra is invariant under flow equivalence of $\lambda$-synchronizing subshifts.

21 pages

Cited by in corpus (1)

• Flow equivalence of sofic shifts