Quaternionic functional calculus, grothendieck Rings, and C*-algebras
| dc.contributor.advisor | Kučerovský, Dan Z. | |
| dc.contributor.author | Ghamari, Elham | |
| dc.date.accessioned | 2024-10-15T16:42:22Z | |
| dc.date.available | 2024-10-15T16:42:22Z | |
| dc.date.issued | 2024-08 | |
| dc.description.abstract | This dissertation is organized into two parts. In the first part, we extend the Gelfand theorem, typically applicable only in commutative scenarios, to quaternion C∗-algebras. Moreover, we delve into the computation of K-groups for quaternion UHF-algebras. Surprisingly, our findings reveal that evaluating these K-groups can be effectively achieved by solely considering the real part of the quaternion UHF-algebra. The second part introduces a captivating construction by Grothendieck, originally formulated for algebraic varieties, and innovatively adapts it to the realm of C∗-algebras. We pay particular attention to the existence of nontrivial characters, further enriching our understanding of these algebras. | |
| dc.description.copyright | © Elham Ghamari, 2024 | |
| dc.format.extent | vii, 100 | |
| dc.format.medium | electronic | |
| dc.identifier.uri | https://unbscholar.lib.unb.ca/handle/1882/38156 | |
| dc.language.iso | en | |
| dc.publisher | University of New Brunswick | |
| dc.rights | http://purl.org/coar/access_right/c_abf2 | |
| dc.subject.discipline | Mathematics and Statistics | |
| dc.title | Quaternionic functional calculus, grothendieck Rings, and C*-algebras | |
| dc.type | doctoral thesis | |
| oaire.license.condition | other | |
| thesis.degree.discipline | Mathematics and Statistics | |
| thesis.degree.grantor | University of New Brunswick | |
| thesis.degree.level | doctorate | |
| thesis.degree.name | Ph.D. |