$C^*$-algebras associated with lambda-synchronizing subshifts and flow equivalence

TL;DR

This paper investigates the algebraic structures of $C^*$-algebras linked to $\lambda$-synchronizing subshifts, demonstrating their invariance under flow equivalence, and introduces $\lambda$-graph systems as a key tool.

Contribution

It introduces $\lambda$-synchronizing $\lambda$-graph systems and proves the invariance of associated $C^*$-algebras under flow equivalence for these subshifts.

Findings

The $C^*$-algebra's stable isomorphism class is invariant under flow equivalence.

$\lambda$-graph systems serve as a left Fischer cover analogue for $\lambda$-synchronizing subshifts.

The algebraic structure of these $C^*$-algebras is characterized and studied.

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 $C^*$-algebra associated with the $\lambda$-synchronizing $\lambda$-graph system and prove that the stable isomorphism class of the $C^*$-algebra with its Cartan subalgebra is invariant under flow equivalence of $\lambda$-synchronizing subshifts.