Browsing by Author "Ghamari, Elham"

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    Quaternionic functional calculus, grothendieck Rings, and C*-algebras
    (University of New Brunswick, 2024-08) Ghamari, Elham; Kučerovský, Dan Z.
    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.