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All Irrational Extended Rotation Algebras are AF Algebras

Published online by Cambridge University Press:  20 November 2018

George A. Elliott  and
Zhuang Niu
George A. Elliott
Affiliation:
Department of Mathematics, University of Toronto, Toronto, ON M5S 2E4 e-mail: [email protected]
Zhuang Niu
Affiliation:
Department of Mathematics, University of Wyoming, Laramie, WY 82071, USA e-mail: [email protected]
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Abstract

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Let $\theta \,\in \,\left[ 0,\,1 \right]$ be any irrational number. It is shown that the extended rotation algebra ${{B}_{\theta }}$ introduced by the authors in J. Reine Angew. Math. 665(2012), pp. 1–71, is always an $\text{AF}$ algebra.

Keywords

46L0546L3546L5546L80irrational rotation algebraextended irrational rotation algebraAF-embedding.
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 67 , Issue 4 , 01 August 2015 , pp. 810 - 826
Copyright
Copyright © Canadian Mathematical Society 2015

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