Journal of Operator Theory

Volume 58, Issue 2, Fall 2007 pp. 311-349.

Classification theorem for direct limits of extensions of circle algebras by purely infinite $C^*$-algebras

Authors: Efren Ruiz
Author institution: Department of Mathematics, University of Toronto, Toronto, M5S 2E4, Canada and Department of Mathematics, University of Hawaii Hilo, 200 W. Kawili St., Hilo, Hawaii 96720, USA

Summary: We give a classification theorem for a class of $C^*$-algebras which are direct limits of finite direct sums of $\mathcal{E}_{0}$-algebras. The invariant consists of the following: (1) the set of Murray-von Neumann equivalence classes of projections; (2) the set of homotopy classes of hyponormal partial isometries; (3) a map $d$; and (4) total $K$-theory.

Keywords: Classification, nuclear $C^*$-algebras, extensions

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