The primitive spectrum of C*-algebras of etale groupoids with abelian isotropy
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915181994442752 |
|---|---|
| author | Christensen, Johannes Neshveyev, Sergey |
| author_facet | Christensen, Johannes Neshveyev, Sergey |
| contents | Given a Hausdorff locally compact étale groupoid $\mathcal G$, we describe as a topological space the part of the primitive spectrum of $C^*(\mathcal G)$ obtained by inducing one-dimensional representations of amenable isotropy groups of $\mathcal G$. When $\mathcal G$ is amenable, second countable, with abelian isotropy groups, our result gives the description of $\operatorname{Prim} C^*(\mathcal G)$ conjectured by van Wyk and Williams. This, in principle, completely determines the ideal structure of a large class of separable C$^*$-algebras, including the transformation group C$^*$-algebras defined by amenable actions of discrete groups with abelian stabilizers and the C$^*$-algebras of higher rank graphs. As an illustration we describe the primitive spectrum of the C$^*$-algebra of any row-finite higher rank graph without sources. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_02025 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The primitive spectrum of C*-algebras of etale groupoids with abelian isotropy Christensen, Johannes Neshveyev, Sergey Operator Algebras Given a Hausdorff locally compact étale groupoid $\mathcal G$, we describe as a topological space the part of the primitive spectrum of $C^*(\mathcal G)$ obtained by inducing one-dimensional representations of amenable isotropy groups of $\mathcal G$. When $\mathcal G$ is amenable, second countable, with abelian isotropy groups, our result gives the description of $\operatorname{Prim} C^*(\mathcal G)$ conjectured by van Wyk and Williams. This, in principle, completely determines the ideal structure of a large class of separable C$^*$-algebras, including the transformation group C$^*$-algebras defined by amenable actions of discrete groups with abelian stabilizers and the C$^*$-algebras of higher rank graphs. As an illustration we describe the primitive spectrum of the C$^*$-algebra of any row-finite higher rank graph without sources. |
| title | The primitive spectrum of C*-algebras of etale groupoids with abelian isotropy |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2405.02025 |