Journal of Operator Theory

Volume 35, Issue 1, Winter 1996 pp. 147-178.

On the classification of C*-algebras of real rank zero with zero K_1

Authors: Huaxin Lin
Author institution:Department of Mathematics, University of Oregon, Eugene, OR 97403-1222, U.S.A.

Summary: A classification of certain separable C*-algebras of real rank zero with trivial K_1-group is given. The C*-algebras considered are those that can be expressed as direct limits of direct sums of matrix algebras, matrix algebras over Cuntz-algebras and matrix algebras over corners of certain extensions of Cuntz-algebras by the compact operators. C*-algebras in the class are not necessary simple. They are, in general, neither finite nor purely infinite. However, the class includes all AF-algebras and all separable nuclear purely infinite simple C*-algebras with UCT and trivial K_1. It is closed under stable isomorphism, quotients, hereditary C*-subalgebras, direct limits and tensor products with AF-algebras.

Keywords: C*-algebras, real rank zero, classification.

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