by Ara, P.; Moreno, M. A.; Pardo, E.

We compute the monoid V(L

_K
(E)) of isomorphism classes of finitely generated projective modules over certain graph algebras L

_K
(E), and we show that this monoid satisfies the refinement property and separative cancellation. We also show that there is a natural isomorphism between the lattice of graded ideals of L

_K
(E) and the lattice of order-ideals of V(L

_K
(E)). When K is the field $\mathbb C$ of complex numbers, the algebra $L_{\mathbb C}(E)$ is a dense subalgebra of the graph C
^*-algebra C
^*(E), and we show that the inclusion map induces an isomorphism between the corresponding monoids. As a consequence, the graph C*-algebra of any row-finite graph turns out to satisfy the stable weak cancellation property.

DOI: 10.1007/s10468-006-9044-z
Online Date: 11/25/2006
Print publication date: 4/1/2007
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