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${C}^{\ast } $-ALGEBRAS ASSOCIATED WITH LAMBDA-SYNCHRONIZING SUBSHIFTS AND FLOW EQUIVALENCE
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 95 / Issue 2 / October 2013
- Published online by Cambridge University Press:
- 07 August 2013, pp. 241-265
- Print publication:
- October 2013
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- Article
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- You have access
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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.
