On the C*-algebra associated with the full adele ring of a number field
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866916576074137600 |
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| author | Bruce, Chris Takeishi, Takuya |
| author_facet | Bruce, Chris Takeishi, Takuya |
| contents | The multiplicative group of a number field acts by multiplication on the full adele ring of the field. Generalising a theorem of Laca and Raeburn, we explicitly describe the primitive ideal space of the crossed product C*-algebra associated with this action. We then distinguish real, complex, and finite places of the number field using K-theoretic invariants. Combining these results with a recent rigidity theorem of the authors implies that any *-isomorphism between two such C*-algebras gives rise to an isomorphism of the underlying number fields that is constructed from the *-isomorphism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_10857 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the C*-algebra associated with the full adele ring of a number field Bruce, Chris Takeishi, Takuya Operator Algebras Number Theory 46L05, 46L80 (Primary) 11R04, 11R56, 46L35 (Secondary) The multiplicative group of a number field acts by multiplication on the full adele ring of the field. Generalising a theorem of Laca and Raeburn, we explicitly describe the primitive ideal space of the crossed product C*-algebra associated with this action. We then distinguish real, complex, and finite places of the number field using K-theoretic invariants. Combining these results with a recent rigidity theorem of the authors implies that any *-isomorphism between two such C*-algebras gives rise to an isomorphism of the underlying number fields that is constructed from the *-isomorphism. |
| title | On the C*-algebra associated with the full adele ring of a number field |
| topic | Operator Algebras Number Theory 46L05, 46L80 (Primary) 11R04, 11R56, 46L35 (Secondary) |
| url | https://arxiv.org/abs/2209.10857 |