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June 2021 A remark on the freeness condition of Suzuki's correspondence theorem for intermediate C$^*$-algebras
Ryo OCHI
Hokkaido Math. J. 50(2): 247-262 (June 2021). DOI: 10.14492/hokmj/2019-105

Abstract

Let $\Gamma$ be a discrete group satisfying the approximation property (AP). Let $X$, $Y$ be $\Gamma$-spaces and $\pi \colon Y \to X$ be a proper factor map which is injective on the non-free part. We prove the one-to-one correspondence between intermediate C$^*$-algebras of $C_0(X) \rtimes_r \Gamma \subset C_0(Y) \rtimes_r \Gamma$ and intermediate $\Gamma$-${\rm C}^\ast$-algebras of $C_0(X) \subset C_0(Y)$. This is a generalization of Suzuki's theorem that proves the statement for free actions.

Acknowledgment

The author would like to thank his supervisor, Professor Narutaka Ozawa for his support and many valuable comments. He also thanks Professor Yuhei Suzuki for valuable comments and suggesting Example 24 and the arguments following it.

Citation

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Ryo OCHI. "A remark on the freeness condition of Suzuki's correspondence theorem for intermediate C$^*$-algebras." Hokkaido Math. J. 50 (2) 247 - 262, June 2021. https://doi.org/10.14492/hokmj/2019-105

Information

Received: 24 January 2019; Revised: 24 February 2019; Published: June 2021
First available in Project Euclid: 27 August 2021

Digital Object Identifier: 10.14492/hokmj/2019-105

Subjects:
Primary: ‎37B05‎, 46L05

Rights: Copyright c 2021 Hokkaido University, Department of Mathematics

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Vol.50 • No. 2 • June 2021
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