Approximately finite-dimensional $C^*$-algebras with projective Hilbert modules, their Bratteli diagrams, and $K_0$-groups
Sbornik. Mathematics, Tome 188 (1997) no. 10, pp. 1543-1560
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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.
@article{SM_1997_188_10_a5,
author = {A. Ya. Helemskii},
title = {Approximately finite-dimensional $C^*$-algebras with projective {Hilbert} modules, their {Bratteli} diagrams, and $K_0$-groups},
journal = {Sbornik. Mathematics},
pages = {1543--1560},
publisher = {mathdoc},
volume = {188},
number = {10},
year = {1997},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1997_188_10_a5/}
}
TY - JOUR AU - A. Ya. Helemskii TI - Approximately finite-dimensional $C^*$-algebras with projective Hilbert modules, their Bratteli diagrams, and $K_0$-groups JO - Sbornik. Mathematics PY - 1997 SP - 1543 EP - 1560 VL - 188 IS - 10 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/SM_1997_188_10_a5/ LA - en ID - SM_1997_188_10_a5 ER -
%0 Journal Article %A A. Ya. Helemskii %T Approximately finite-dimensional $C^*$-algebras with projective Hilbert modules, their Bratteli diagrams, and $K_0$-groups %J Sbornik. Mathematics %D 1997 %P 1543-1560 %V 188 %N 10 %I mathdoc %U http://geodesic.mathdoc.fr/item/SM_1997_188_10_a5/ %G en %F SM_1997_188_10_a5
A. Ya. Helemskii. Approximately finite-dimensional $C^*$-algebras with projective Hilbert modules, their Bratteli diagrams, and $K_0$-groups. Sbornik. Mathematics, Tome 188 (1997) no. 10, pp. 1543-1560. http://geodesic.mathdoc.fr/item/SM_1997_188_10_a5/