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PRIMITIVE IDEAL SPACE OF $C^*(R_+)\rtimes R^\times $

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  26 December 2024

XIAOHUI CHEN Open the ORCID record for XIAOHUI CHEN [Opens in a new window]  and
HUI LI Open the ORCID record for HUI LI [Opens in a new window]
XIAOHUI CHEN
Affiliation:
Department of Mathematics and Physics, North China Electric Power University, Beijing 102206, PR China e-mail: xiaohui20720@126.com
HUI LI*
Affiliation:
Department of Mathematics and Physics, North China Electric Power University, Beijing 102206, PR China e-mail: 50902471@ncepu.edu.cn
*
e-mail: lihui8605@hotmail.com
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Abstract

For an integral domain R satisfying certain conditions, we characterise the primitive ideal space and its Jacobson topology for the semigroup crossed product $C^*(R_+) \rtimes R^\times $. We illustrate the result by the example $R=\mathbb {Z}[\sqrt {-3}]$.

Keywords

ringsemigroup crossed productcrossed productprimitive ideal

MSC classification

Primary: 46L05: General theory of $C^*$-algebras

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 112 , Issue 2 , October 2025 , pp. 345 - 354
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

The second author was supported by Fundamental Research Funds for the Central Universities (Grant No. 2023MS076).

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