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An infinite C*-algebra with a dense, stably finite *-subalgebra


Authors: Niels Jakob Laustsen and Jared T. White
Journal: Proc. Amer. Math. Soc. 146 (2018), 2523-2528
MSC (2010): Primary 46L05; Secondary 20M25, 46L09
DOI: https://doi.org/10.1090/proc/13931
Published electronically: March 9, 2018
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Abstract: We construct a unital pre-C*-algebra $ A_0$ which is stably finite, in the sense that every left invertible square matrix over $ A_0$ is right invertible, while the C*-completion of $ A_0$ contains a nonunitary isometry, and so it is infinite.


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Additional Information

Niels Jakob Laustsen
Affiliation: Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, United Kingdom
Email: n.laustsen@lancaster.ac.uk

Jared T. White
Affiliation: Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, United Kingdom
Email: j.white6@lancaster.ac.uk

DOI: https://doi.org/10.1090/proc/13931
Keywords: C*-algebra, stably finite, infinite, completion, free product
Received by editor(s): May 4, 2017
Received by editor(s) in revised form: August 14, 2017
Published electronically: March 9, 2018
Communicated by: Adrian Ioana
Article copyright: © Copyright 2018 American Mathematical Society

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