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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
Norio Nawata*
Affiliation:
Graduate School of Mathematics, Kyushu University, Motooka, Fukuoka, 819-0395, Japan email: n-nawata@math.kyushu-u.ac.jp
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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.

Keywords

46L0546L0846L35fundamental groupPicard groupHilbert modulecountable basisstably projectionless algebradimension function
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 64 , Issue 3 , 01 June 2012 , pp. 573 - 587
Copyright
Copyright © Canadian Mathematical Society 2012

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