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Transactions of the American Mathematical Society

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An approximate universal coefficient theorem

Author: Huaxin Lin
Journal: Trans. Amer. Math. Soc. 357 (2005), 3375-3405
MSC (2000): Primary 46L05, 46L35, 46L80
Published electronically: March 25, 2005
MathSciNet review: 2135753
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Abstract: An approximate Universal Coefficient Theorem (AUCT) for certain $C^*$-algebras is established. We present a proof that Kirchberg-Phillips's classification theorem for separable nuclear purely infinite simple $C^*$-algebras is valid for $C^*$-algebras satisfying the AUCT instead of the UCT. It is proved that two versions of AUCT are in fact the same. We also show that $C^*$-algebras that are locally approximated by $C^*$-algebras satisfying the AUCT satisfy the AUCT. As an application, we prove that certain simple $C^*$-algebras which are locally type I are in fact isomorphic to simple AH-algebras. As another application, we show that a sequence of residually finite-dimensional $C^*$-algebras which are asymptotically nuclear and which asymptotically satisfies the AUCT can be embedded into the same simple AF-algebra.

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Additional Information

Huaxin Lin
Affiliation: Department of Mathematics, East China Normal University, Shanghai, People’s Republic of China
Address at time of publication: Department of Mathematics, University of Oregon, Eugene, Oregon 97403-1222

Keywords: Approximate universal coefficient theorem
Received by editor(s): October 1, 2002
Received by editor(s) in revised form: March 12, 2004
Published electronically: March 25, 2005
Additional Notes: This research was partially supported by NSF grants DMS 0097903 and 0355273
Article copyright: © Copyright 2005 American Mathematical Society

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