The primitive spectrum of C*-algebras of etale groupoids with abelian isotropy
| Autor: | Christensen, Johannes, Neshveyev, Sergey |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | Given a Hausdorff locally compact \'etale 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. Comment: 29 pages; v2: minor changes and corrections |
| Databáze: | arXiv |
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