Duke Mathematical Journal

Classification of simple C*-algebras of tracial topological rank zero

Huaxin Lin

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We give a classification theorem for unital separable simple nuclear C*-algebras with tracial topological rank zero which satisfy the universal coefficient theorem. Let A and B be two such C*-algebras. We prove that AB if and only if

(K0(A), K0(A)+, [1A], K1(A)) ≌ K0(B), K0(B)+, [1B], K1(B)).

Article information

Duke Math. J., Volume 125, Number 1 (2004), 91-119.

First available in Project Euclid: 25 September 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46L05: General theory of $C^*$-algebras 46L35: Classifications of $C^*$-algebras
Secondary: 46L80: $K$-theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22]


Lin, Huaxin. Classification of simple C * -algebras of tracial topological rank zero. Duke Math. J. 125 (2004), no. 1, 91--119. doi:10.1215/S0012-7094-04-12514-X. https://projecteuclid.org/euclid.dmj/1096128235

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