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arXiv · 2505.00587

The Hao-Ng isomorphism theorem for reduced crossed products

Adam Dor-On·Ian Thompson
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Abstract

We prove the Hao-Ng isomorphism for reduced crossed products by locally compact Hausdorff groups. More precisely, for a non-degenerate $\mathrm{C}^*$-correspondence $X$ and a generalized gauge action $G \curvearrowright X$ by a locally compact Hausdorff group $G$, we prove the commutation ${\mathcal{O}}_{X\rtimes_rG}\cong {\mathcal{O}}_X\rtimes_rG$ of the reduced crossed product with the Cuntz-Pimsner C*-algebra construction. This is done by proving that the reduced crossed product of an operator algebra commutes with the C*-envelope, which relies on refined W*-dynamical covers of C*-dynamical systems, unitary implementation of W*-dynamical systems, and an operator-valued extension of Maharam's lifting theorem.

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Adam Dor-On, Ian Thompson. 2025-05-01. The Hao-Ng isomorphism theorem for reduced crossed products. https://arxiv.org/abs/2505.00587

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