1 results
Fundamental Group of Simple C*-algebras with Unique Trace III
-
- Journal:
- Canadian Journal of Mathematics / Volume 64 / Issue 3 / 01 June 2012
- Published online by Cambridge University Press:
- 20 November 2018, pp. 573-587
- Print publication:
- 01 June 2012
-
- Article
-
- You have access
- Export citation
-
We introduce the fundamental group
$\mathcal{F}\left( A \right)$ of a simple 
$\sigma $-unital 
${{C}^{*}}$–algebra 
$A$ with unique (up to scalar multiple) densely defined lower semicontinuous trace. This is a generalization of Fundamental Group of Simple${{C}^{*}}$-algebras with Unique Trace I and II by Nawata and Watatani. 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 in Nawata and Watatani. This study is motivated by the work of Kishimoto and Kumjian.
