2004/12/13 by P. Ara, Pere Ara, M. A. Moreno +5 · 8 citations
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #math.OA #math.RA #msc:06A12 #msc:06F05 #msc:16D70 #msc:46L35 #msc:46L80
paper · pdf · doi:10.48550/arxiv.math/0412243
Final version, to appear in "Algebra and Representation Theory"
arxiv created 2006/10/08 · arxiv updated 2009/12/01
We compute the monoid V(LK(E)) of isomorphism classes of finitely generated projective modules over certain graph algebras LK(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 LK(E) and the lattice of order-ideals of V(LK(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.