Geodesic
Classification of simple $C^{*}$-algebras and higher dimensional noncommutative tori
Huaxin Lin1
1 Department of Mathematics, University of Oregon, Eugene, OR 97403, United States
Annals of mathematics, Tome 157 (2003) no. 2, pp. 521-544.

Voir la notice de l'article provenant de la source Annals of Mathematics website

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 noncommutative tori of the form $C({\Bbb T}^k)\times_{\theta}{\Bbb Z}$ are in fact inductive limits of circle algebras.
DOI : 10.4007/annals.2003.157.521

Huaxin Lin 1

1 Department of Mathematics, University of Oregon, Eugene, OR 97403, United States 
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Huaxin Lin. Classification of simple $C^{*}$-algebras and higher dimensional noncommutative tori. Annals of mathematics, Tome 157 (2003) no. 2, pp. 521-544. doi : 10.4007/annals.2003.157.521. http://geodesic.mathdoc.fr/articles/10.4007/annals.2003.157.521/

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