Abstract view
The Bockstein Map is Necessary


Published:19990901
Printed: Sep 1999
Marius Dădărlat
Søren Eilers
Abstract
We construct two nonisomorphic nuclear, stably finite,
real rank zero $C^\ast$algebras $E$ and $E'$ for which
there is an isomorphism of ordered groups
$\Theta\colon \bigoplus_{n \ge 0} K_\bullet(E;\ZZ/n) \to
\bigoplus_{n \ge 0} K_\bullet(E';\ZZ/n)$ which is compatible
with all the coefficient transformations. The $C^\ast$algebras
$E$ and $E'$ are not isomorphic since there is no $\Theta$
as above which is also compatible with the Bockstein operations.
By tensoring with Cuntz's algebra $\OO_\infty$ one obtains a pair
of nonisomorphic, real rank zero, purely infinite $C^\ast$algebras
with similar properties.
Keywords: 
$K$theory, torsion coefficients, natural transformations, Bockstein maps, $C^\ast$algebras, real rank zero, purely infinite, classification
$K$theory, torsion coefficients, natural transformations, Bockstein maps, $C^\ast$algebras, real rank zero, purely infinite, classification

MSC Classifications: 
46L35, 46L80, 19K14 show english descriptions
Classifications of $C^*$algebras $K$theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22] $K_0$ as an ordered group, traces
46L35  Classifications of $C^*$algebras 46L80  $K$theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22] 19K14  $K_0$ as an ordered group, traces
