All Irrational Extended Rotation Algebras are AF Algebras

George A. Elliott; Zhuang Niu

doi:10.4153/cjm-2014-022-5

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All Irrational Extended Rotation Algebras are AF Algebras

George A. Elliott Zhuang Niu

Year: 2014 Journal: Canadian Journal of Mathematics Vol: 67 (4)Pages: 810-826 Publisher: Cambridge University Press

DOI: 10.4153/cjm-2014-022-5

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Abstract

Abstract Let θ ∊ [0, 1] be any irrational number. It is shown that the extended rotation algebra Bθ introduced by the authors in J. Reine Angew. Math. 665(2012), pp. 1–71, is always an AF algebra.

Keywords:

Irrational number Mathematics Rotation (mathematics) Algebra over a field Pure mathematics Geometry

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Advanced Topics in Algebra

Physical Sciences → Mathematics → Algebra and Number Theory

Advanced Operator Algebra Research

Physical Sciences → Mathematics → Mathematical Physics

Algebraic structures and combinatorial models

Physical Sciences → Mathematics → Geometry and Topology

All Irrational Extended Rotation Algebras are AF Algebras

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