Algebras and Representation Theory

, Volume 10, Issue 2, pp 157-178

First online:

Nonstable K-theory for Graph Algebras

  • P. AraAffiliated withDepartament de Matemàtiques, Universitat Autònoma de Barcelona Email author 
  • , M. A. MorenoAffiliated withDepartamento de Matemáticas, Universidad de Cádiz
  • , E. PardoAffiliated withDepartamento de Matemáticas, Universidad de Cádiz

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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.

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