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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