Classification of simple C*-algebras and higher dimensional noncommutative tori

2003/11/24 by Huaxin Lin
Mathematics · #math.OA #math.FA

paper · pdf

published as Ann. of Math. (2), Vol. 157 (2003), no. 2, 521--544 · 24 pages published version

arxiv created 2003/11/24 · arxiv updated 2009/12/01

Abstract

We show that unital simple C*-algebras with tracial topological rank zero which are locally approximated by subhomogeneous C^-algebras can be classified by their ordered K-theory. We apply this classification result to show that certain simple crossed products are isomorphic if they have the same ordered K-theory. In particular, irrational higher dimensional non-commutative tori of the form C(\mathbb T^k)×_θ\mathbb Z are in fact inductive limits of circle algebras.

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