2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/226094We introduce the fundamental group ${\mathcal F}(A)$ of a unital simple $C^*$-algebra $A$ with a unique normalized trace. We compute fundamental groups ${\mathcal F}(A)$ of several nuclear or non-nuclear $C^*$-algebras $A$. K-theoretical obstruction enables us to compute the fundamental group easily. Our study is essentially based on the computation of Picard groups by Kodaka.11 pagesOperator AlgebrasFunctional Analysis46l05; 46l08text