Algebras and Representation Theory

, Volume 10, Issue 2, pp 157–178

Nonstable K-theory for Graph Algebras

Article

Abstract

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.

Key words

graph algebra weak cancellation separative cancellation refinement monoid nonstable K-theory ideal lattice 

Mathematics Subject Classifications (2000)

Primary 16D70 46L35 Secondary 06A12 06F05 46L80 

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Copyright information

© Springer Science + Business Media B.V. 2006

Authors and Affiliations

  1. 1.Departament de MatemàtiquesUniversitat Autònoma de BarcelonaBellaterraSpain
  2. 2.Departamento de MatemáticasUniversidad de CádizPuerto RealSpain

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