Exactness of Cuntz-Pimsner \(C^*\)-algebras (Q2747932)
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scientific article; zbMATH DE number 1658548
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Exactness of Cuntz-Pimsner \(C^*\)-algebras |
scientific article; zbMATH DE number 1658548 |
Statements
9 May 2002
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Hilbert \(C^*\)-bimodule
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exact \(C^*\)-algebra
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Cuntz-Pimsner algebra
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non-commutative entropy
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Brown-Voiculescu topological entropy
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Bogoljubov automorphisms
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0.9275571
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0.9233001
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0.9175042
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0.9080983
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Exactness of Cuntz-Pimsner \(C^*\)-algebras (English)
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For a full Hilbert \(C^*\)-bimodule \(H\) over a \(C^*\)-algebra \(A\), let \(O(H)\) and \(E(H)\) be the Cuntz--Pimsner algebra and the extended Cuntz-Pimsner algebra associated to \(H\) [\textit{M. Pimsner}, Fields Inst. Commun. 12, 189-212 (1997; Zbl 0871.46028)]. It is proved that \(E(H)\) (or \(O(H)\)) is exact iff \(A\) is exact. In the case, when \(A\) is finitedimensional, it is shown that the Brown-Voiculescu topological entropy of Bogoljubov automorphisms of \(E(H)\) is zero.
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