Fundamental group of simple $C^{\ast }$-algebras with unique trace

Abstract

We introduce the fundamental group $\mathcal{F}(A)$ of a unital simple $C^{\ast }$-algebra $A$ with a unique normalized trace. We compute fundamental groups $\mathcal{F}(A)$ of several nuclear or non-nuclear $C^{\ast }$-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 pages

References in corpus (1)

• $C^{\ast }$-algebras associated with real multiplication