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

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

2010-06-29

arxiv.org/abs/1006.5501v2

Mathematics

Operator Algebras

15 pages, Typos are corrected

Scientific paper

We introduce the fundamental group F(A) of a simple $\sigma$-unital $C^*$-algebra $A$ with unique (up to scalar multiple) densely defined lower semicontinuous trace. This is a generalization of our previous works. Our definition in this paper makes sense for stably projectionless $C^*$-algebras. We show that there exist separable stably projectionless $C^*$-algebras such that their fundamental groups are equal to $\mathbb{R}_+^\times$ by using the classification theorem of Razak and Tsang. This is a contrast to the unital case. This study is motivated by the work of Kishimoto and Kumjian.

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