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

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

2011-05-17

arxiv.org/abs/1105.3250v1

Mathematics

Operator Algebras

21 pages

Scientific paper

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.

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