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Fundamental Group of Simple C*-algebras with Unique Trace III

Published online by Cambridge University Press:  20 November 2018

Norio Nawata*
Affiliation:
Graduate School of Mathematics, Kyushu University, Motooka, Fukuoka, 819-0395, Japan email: [email protected]
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Abstract

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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.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2012

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