K-theory for the simple $C^*$-algebra of the Fibonacchi Dyck system

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dc.creatorMatsumoto, Kengo
dc.date2006-07-21
dc.date.accessioned2026-07-07T07:20:46Z
dc.date.available2026-07-07T07:20:46Z
dc.descriptionLet $F$ be the Fibonacci matrix $ \bigl[\begin{smallmatrix} 1 & 1 1 & 0 \\ \end{smallmatrix}\bigr] $. The Fibonacci Dyck shift is a subshsystem of the Dyck shift $D_2$ constrained by the matrix $F$. Let ${{\frak L}^{Ch(D_F)}}$ be a $λ$-graph system presenting the subshift $D_F$, that is called the Cantor horizon $λ$-graph system for $D_F$. We will study the $C^*$-algebra ${\cal O}_{{\frak L}^{Ch(D_F)}}$ associated with $ {{\frak L}^{Ch(D_F)}} $. It is simple purely infinite and generated by four partial isometries with some operator relations. We will compute the K-theory of the $C^*$-algebra. As a result, the $C^*$-algebra is simple purely infinite and not semiprojective. Hence it is not stably isomorphic to any Cuntz-Krieger algebra.
dc.description18pages
dc.identifierhttps://arxiv.org/abs/math/0607519
dc.identifierhttp://arxiv.org/abs/math/0607519
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/115065
dc.subjectOperator Algebras
dc.subjectDynamical Systems
dc.subject46L80;46L55, 37B10
dc.titleK-theory for the simple $C^*$-algebra of the Fibonacchi Dyck system
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