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 language | English |
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Pages (from-to) | 157-178 |
Journal | Algebras and Representation Theory |
Volume | 10 |
DOIs | |
Publication status | Published - 1 Apr 2007 |
Keywords
- Graph algebra
- Ideal lattice
- Nonstable K-theory
- Refinement monoid
- Separative cancellation
- Weak cancellation