Journal Title
Title of Journal: Algebr Represent Theor
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Abbravation: Algebras and Representation Theory
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Publisher
Kluwer Academic Publishers
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Authors: P Ara M A Moreno E Pardo
Publish Date: 2006/11/25
Volume: 10, Issue: 2, Pages: 157-178
Abstract
We compute the monoid VL 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 orderideals of VL K E When K is the field mathbb C of complex numbers the algebra L mathbb CE 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 Calgebra of any rowfinite graph turns out to satisfy the stable weak cancellation propertyThe first author was partially supported by the DGI and European Regional Development Fund jointly through Project BFM200201390 the second and the third by the DGI and European Regional Development Fund jointly through Project MTM200400149 and by PAI III grant FQM298 of the Junta de Andalucía Also the first and third authors are partially supported by the Comissionat per Universitats i Recerca de la Generalitat de Catalunya
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