Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

Request Permissions   Purchase Content 
 

 

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
DOI: https://doi.org/10.1090/S0002-9939-2014-12346-X
Published electronically: July 21, 2014
MathSciNet review: 3251730
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 46L40, 06F20

Retrieve articles in all journals with MSC (2010): 46L40, 06F20


Additional Information

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
Email: nawata@cc.osaka-kyoiku.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-2014-12346-X
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