A Uniqueness Theorem for C*-algebras of Hausdorff Étale Groupoids
| dc.contributor.author | Goerke, Gavin | |
| dc.contributor.supervisor | Laca, Marcelo | |
| dc.contributor.supervisor | Eagle, Christopher | |
| dc.date.accessioned | 2023-04-27T20:58:52Z | |
| dc.date.available | 2023-04-27T20:58:52Z | |
| dc.date.copyright | 2023 | en_US |
| dc.date.issued | 2023-04-27 | |
| dc.degree.department | Department of Mathematics and Statistics | |
| dc.degree.level | Master of Science M.Sc. | en_US |
| dc.description.abstract | In this thesis we study the ideal intersection property for inclusions of C*-algebras C*(H)↪C*(G) induced from a family of open subgroupoids {H} of a locally compact Hausdorff étale groupoid G. For such a family of open subgroupoids we define the notion of relative topological principality and we show that if G is relatively topologically principal to {H} then a representation of C*(G) is faithful if and only if the restriction of the representation to each of the subalgebras C*(H) is faithful. This gives a new method of verifying injectivity of representations of reduced groupoid C*-algebras. As an application of our result we prove a uniqueness theorem for C*-algebras of left cancellative small categories which generalizes a theorem of Marcelo Laca and Camila Sehnem for Toeplitz algebras of group embeddable monoids. | en_US |
| dc.description.scholarlevel | Graduate | en_US |
| dc.identifier.uri | http://hdl.handle.net/1828/15010 | |
| dc.language | English | eng |
| dc.language.iso | en | en_US |
| dc.rights | Available to the World Wide Web | en_US |
| dc.subject | C*-algebras | en_US |
| dc.subject | groupoid | en_US |
| dc.subject | topologically free | en_US |
| dc.title | A Uniqueness Theorem for C*-algebras of Hausdorff Étale Groupoids | en_US |
| dc.type | Thesis | en_US |