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# All Irrational Extended Rotation Algebras are AF Algebras

Published:2014-09-15

• George A. Elliott,
Department of Mathematics, University of Toronto, Toronto, ON M5S 2E4
• Zhuang Niu,
Department of Mathematics, University of Wyoming, Laramie, WY 82071, USA
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## Abstract

Let $\theta\in[0, 1]$ be any irrational number. It is shown that the extended rotation algebra $\mathcal B_\theta$ introduced in a previous paper is always an AF algebra.
 Keywords: irrational rotation algebra, extended irrational rotation algebra, AF-embedding