Abstract view
The Ordered $K$theory of a Full Extension


Published:20130711
Printed: Jun 2014
Søren Eilers,
Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, DK2100 Copenhagen, Denmark
Gunnar Restorff,
Faculty of Science and Technology, University of Faroe Islands, Nóatún 3, FO100 Tórshavn, Faroe Islands
Efren Ruiz,
Department of Mathematics, University of Hawaii, Hilo, 200 W. Kawili St., Hilo, Hawaii, 967204091 USA
Abstract
Let $\mathfrak{A}$ be a $C^{*}$algebra with real rank zero which has
the stable weak cancellation property. Let $\mathfrak{I}$ be an ideal
of $\mathfrak{A}$ such that $\mathfrak{I}$ is stable and satisfies the
corona factorization property. We prove that
$
0 \to \mathfrak{I} \to \mathfrak{A} \to \mathfrak{A} / \mathfrak{I} \to 0
$
is a full extension if and only if the extension is stenotic and
$K$lexicographic. {As an immediate application, we extend the
classification result for graph $C^*$algebras obtained by Tomforde
and the first named author to the general nonunital case. In
combination with recent results by Katsura, Tomforde, West and the
first author, our result may also be used to give a purely
$K$theoretical description of when an essential extension of two
simple and stable graph $C^*$algebras is again a graph
$C^*$algebra.}
MSC Classifications: 
46L80, 46L35, 46L05 show english descriptions
$K$theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22] Classifications of $C^*$algebras General theory of $C^*$algebras
46L80  $K$theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22] 46L35  Classifications of $C^*$algebras 46L05  General theory of $C^*$algebras
