Isotropy fibers of ideals in groupoid C$^{*}$-algebras
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866911895738384384 |
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| author | Christensen, Johannes Neshveyev, Sergey |
| author_facet | Christensen, Johannes Neshveyev, Sergey |
| contents | Given a locally compact étale groupoid and an ideal $I$ in its groupoid C$^*$-algebra, we show that $I$ defines a family of ideals in group C$^*$-algebras of the isotropy groups and then study to which extent $I$ is determined by this family. As an application we obtain the following results: (a) prove that every proper ideal is contained in an induced primitive ideal; (b) describe the maximal ideals; (c) classify the primitive ideals for a class of graded groupoids with essentially central isotropy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_10768 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Isotropy fibers of ideals in groupoid C$^{*}$-algebras Christensen, Johannes Neshveyev, Sergey Operator Algebras Given a locally compact étale groupoid and an ideal $I$ in its groupoid C$^*$-algebra, we show that $I$ defines a family of ideals in group C$^*$-algebras of the isotropy groups and then study to which extent $I$ is determined by this family. As an application we obtain the following results: (a) prove that every proper ideal is contained in an induced primitive ideal; (b) describe the maximal ideals; (c) classify the primitive ideals for a class of graded groupoids with essentially central isotropy. |
| title | Isotropy fibers of ideals in groupoid C$^{*}$-algebras |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2308.10768 |