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<jats:p>Given a real number $\beta > 1$, we construct a simple purely infinite $C^*$-algebra ${\cal O}_{\beta}$ as a $C^*$-algebra arising from the $\beta$-subshift in the symbolic dynamics. The $C^*$-algebras $\{{\cal O}_{\beta} \}_{1<\beta \in {\Bbb R}}$ interpolate between the Cuntz algebras $\{{\cal O}_n\}_{1 < n \in {\Bbb N}}$. The K-groups for the $C^*$-algebras ${\cal O}_{\beta}$, $1 < \beta \in {\Bbb R}$, are computed so that they are completely classified up to isomorphism. We prove that the KMS-state for the gauge action on ${\cal O}_{\beta}$ is unique at the inverse temperature $\log \beta$, which is the topological entropy for the $\beta$-shift. Moreover, ${\cal O}_{\beta}$ is realized to be a universal $C^*$-algebra generated by $n-1=[\beta]$ isometries and one partial isometry with mutually orthogonal ranges and a certain relation coming from the sequence of $\beta$-expansion of $1$.</jats:p>
収録刊行物
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- Ergodic Theory and Dynamical Systems
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Ergodic Theory and Dynamical Systems 18 (4), 937-962, 1998-08
Cambridge University Press (CUP)
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詳細情報 詳細情報について
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- CRID
- 1363951793539674240
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- NII論文ID
- 30022887688
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- NII書誌ID
- AA10635922
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- ISSN
- 14694417
- 01433857
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