Ghamari, Elham2024-10-152024-10-152024-08https://unbscholar.lib.unb.ca/handle/1882/38156This 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.vii, 100electronicenhttp://purl.org/coar/access_right/c_abf2doctoral thesisKučerovský, Dan Z.Mathematics and Statistics