Abstract
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
C
of complex numbers, the algebra
L
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.