This article is cited in 2 papers

Approximately finite-dimensional $C^*$-algebras with projective Hilbert modules, their Bratteli diagrams, and $K_0$-groups

A. Ya. Helemskii

M. V. Lomonosov Moscow State University

Abstract: This paper is devoted to the homological classification of approximately finite-dimensional $C^*$-algebras. The algebras in this class for which there exists at least one non-trivial Hilbert module and those for which there exists at least one faithful Hilbert module are described. The description is given in terms of the Bratteli diagrams of the algebras in question and in terms of the ordered $K_0$-groups of these algebras.

UDC: 512.553.7+512.556

MSC: Primary 46L45, 46L80, 42A60; Secondary 46L35, 18G05

Received: 01.10.1996

DOI: 10.4213/sm267

 English version: Sbornik: Mathematics, 1997, 188:10, 1543–1560

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