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

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

2003-11-24

arxiv.org/abs/math/0311415v1

Ann. of Math. (2), Vol. 157 (2003), no. 2, 521--544

Mathematics

Operator Algebras

24 pages published version

Scientific paper

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 $C({\mathbb T}^k)\times_{\theta}{\mathbb Z}$ are in fact inductive limits of circle algebras.

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