Nonstable K-theory for graph algebras

P. Ara, M. A. Moreno, E. Pardo

Research output: Contribution to journalArticleResearchpeer-review

184 Citations (Scopus)

Abstract

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 ℂ of complex numbers, the algebra Lℂ(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. © Springer Science + Business Media B.V. 2007.
Original languageEnglish
Pages (from-to)157-178
JournalAlgebras and Representation Theory
Volume10
DOIs
Publication statusPublished - 1 Apr 2007

Keywords

  • Graph algebra
  • Ideal lattice
  • Nonstable K-theory
  • Refinement monoid
  • Separative cancellation
  • Weak cancellation

Fingerprint Dive into the research topics of 'Nonstable K-theory for graph algebras'. Together they form a unique fingerprint.

Cite this