Ideals of étale groupoid algebras with coefficients in a sheaf with applications to topological dynamics
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916219704049664 |
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| author | de Castro, Gilles G. Gonçalves, Daniel Steinberg, Benjamin |
| author_facet | de Castro, Gilles G. Gonçalves, Daniel Steinberg, Benjamin |
| contents | We prove the Effros-Hahn conjecture for groupoid algebras with coefficients in a sheaf, obtaining as a consequence a description of the ideals in skew inverse semigroup rings. We also use the description of the ideals to characterize when the groupoid algebras with coefficients in a sheaf are von Neumann regular, primitive, semiprimitive, or simple. We apply our results to the topological dynamics of actions of inverse semigroups, describing the existence of dense orbits and minimality in terms of primitivity and simplicity, respectively, of the associated algebra. Moreover, we apply our results to the usual complex groupoid algebra of continuous functions with compact support, used to build the C*-algebra associated with a groupoid, and describe criteria for its simplicity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_15139 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ideals of étale groupoid algebras with coefficients in a sheaf with applications to topological dynamics de Castro, Gilles G. Gonçalves, Daniel Steinberg, Benjamin Rings and Algebras Dynamical Systems Operator Algebras We prove the Effros-Hahn conjecture for groupoid algebras with coefficients in a sheaf, obtaining as a consequence a description of the ideals in skew inverse semigroup rings. We also use the description of the ideals to characterize when the groupoid algebras with coefficients in a sheaf are von Neumann regular, primitive, semiprimitive, or simple. We apply our results to the topological dynamics of actions of inverse semigroups, describing the existence of dense orbits and minimality in terms of primitivity and simplicity, respectively, of the associated algebra. Moreover, we apply our results to the usual complex groupoid algebra of continuous functions with compact support, used to build the C*-algebra associated with a groupoid, and describe criteria for its simplicity. |
| title | Ideals of étale groupoid algebras with coefficients in a sheaf with applications to topological dynamics |
| topic | Rings and Algebras Dynamical Systems Operator Algebras |
| url | https://arxiv.org/abs/2404.15139 |