Fundamental group of simple $C^*$-algebras with unique trace

Details Fundamental group of simple $C^*$-algebras with unique trace Fundamental group of simple $C^*$-algebras with unique trace

2009-04-07

arxiv.org/abs/0904.1081v1

Mathematics

Operator Algebras

11 pages

Scientific paper

We 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.

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