Algebras and Representation Theory

, Volume 10, Issue 2, pp 157–178

Nonstable K-theory for Graph Algebras

Authors

    • Departament de MatemàtiquesUniversitat Autònoma de Barcelona
  • M. A. Moreno
    • Departamento de MatemáticasUniversidad de Cádiz
  • E. Pardo
    • Departamento de MatemáticasUniversidad de Cádiz
Article

DOI: 10.1007/s10468-006-9044-z

Cite this article as:
Ara, P., Moreno, M.A. & Pardo, E. Algebr Represent Theor (2007) 10: 157. doi:10.1007/s10468-006-9044-z

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 algebraweak cancellationseparative cancellationrefinement monoidnonstable K-theoryideal lattice

Mathematics Subject Classifications (2000)

Primary 16D7046L35Secondary 06A1206F0546L80
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© Springer Science + Business Media B.V. 2006