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arXiv · 1905.10473

Hyperrigidity of C*-correspondences

Se-Jin Kim
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Abstract

We show that hyperrigidity for a C*-correspondence $(A,X)$ is equivalent to non-degeneracy of the left action of the Katsura ideal $\mathcal{J}_X$ on $X$. Due to the work of Katsoulis and Ramsey, our result shows that if $G$ is a locally compact group acting on $(A,X)$ and the Katsura ideal $\mathcal{J}_X$ acts on $X$ non-degenerately then the Hao-Ng isomorphism problem for reduced crossed products has a positive solution and the Hao-Ng isomorphism problem for full crossed products has a partial solution.

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Se-Jin Kim. 2019-05-24. Hyperrigidity of C*-correspondences. https://arxiv.org/abs/1905.10473

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