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A note on trace scaling actions and fundamental groups of C$ ^*$-algebras

Author: Norio Nawata
Journal: Proc. Amer. Math. Soc. 142 (2014), 3903-3908
MSC (2010): Primary 46L40; Secondary 06F20
Published electronically: July 21, 2014
MathSciNet review: 3251730
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Abstract: Using the Effros-Handelman-Shen theorem and Elliott's classification theorem of AF algebras, we show that there exists a unital simple AF algebra $ A$ with unique trace such that $ A\otimes \mathbb{K}$ admits no trace scaling action of the fundamental group of $ A$.

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Norio Nawata
Affiliation: Department of Mathematics and Informatics, Graduate school of Science, Chiba University, 1-33 Yayoi-cho, Inage, Chiba, 263-8522, Japan
Address at time of publication: Department of Arts and Sciences, Osaka Kyoiku University, 4-698-1 Asahigaoka, Kashiwara, Osaka, 582-8582, Japan

Keywords: Fundamental group, trace scaling action, dimension group, Effros-Handelman-Shen theorem
Received by editor(s): January 4, 2012
Received by editor(s) in revised form: December 12, 2012
Published electronically: July 21, 2014
Additional Notes: The author is a Research Fellow of the Japan Society for the Promotion of Science.
Communicated by: Marius Junge
Article copyright: © Copyright 2014 American Mathematical Society

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