Cuntz-Pimsner \(C^*\)-algebras and crossed products by Hilbert \(C^*\)-bimodules. (English) Zbl 1181.46040
Summary: Given a correspondence \(X\) over a \(C^*\)-algebra \(A\), we construct a \(C^*\)-algebra \(A^X_\infty\) and a Hilbert \(C^*\)-bimodule \(X_\infty\), over \(A^X_\infty\) such that the augmented Cuntz-Pimsner \(C^*\)-algebras \(\widetilde{\mathcal O}_X\) and the crossed product \(A^X_\infty\rtimes X_\infty\) are isomorphic. This construction enables us to establish a condition for two augmented Cuntz-Pimsner \(C^*\)-algebras to be Morita equivalent.
References:
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