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${C}^{\ast } $-ALGEBRAS ASSOCIATED WITH LAMBDA-SYNCHRONIZING SUBSHIFTS AND FLOW EQUIVALENCE

Part of: Selfadjoint operator algebras Topological dynamics

Published online by Cambridge University Press:  07 August 2013

KENGO MATSUMOTO
KENGO MATSUMOTO*
Affiliation:
Department of Mathematics, Joetsu University of Education, Joetsu 943-8512, Japan
*
kengo@juen.ac.jp
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Abstract

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The class of $\lambda $-synchronizing subshifts generalizes the class of irreducible sofic shifts. A $\lambda $-synchronizing subshift can be presented by a certain $\lambda $-graph system, called the $\lambda $-synchronizing $\lambda $-graph system. The $\lambda $-synchronizing $\lambda $-graph system of a $\lambda $-synchronizing subshift can be regarded as an analogue of the Fischer cover of an irreducible sofic shift. We will study algebraic structure of the ${C}^{\ast } $-algebra associated with a $\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.

Keywords

subshiftsC∗-algebrasλ-graph systemsflow equivalenceK-groupsBowen–Franks groupsλ-synchronization

MSC classification

Secondary: 46L35: Classifications of $C^*$-algebras 37B10: Symbolic dynamics 46L80: $K$-theory and operator algebras (including cyclic theory)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 95 , Issue 2 , October 2013 , pp. 241 - 265
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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