Nonstable $K$-theory for graph algebras
| dc.creator | Ara, P. | |
| dc.creator | Moreno, M. A. | |
| dc.creator | Pardo, E. | |
| dc.date | 2004-12-13 | |
| dc.date | 2006-10-08 | |
| dc.date.accessioned | 2026-07-07T06:39:09Z | |
| dc.date.available | 2026-07-07T06:39:09Z | |
| dc.description | 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. | |
| dc.description | Final version, to appear in "Algebra and Representation Theory" | |
| dc.identifier | https://arxiv.org/abs/math/0412243 | |
| dc.identifier | http://arxiv.org/abs/math/0412243 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/100978 | |
| dc.subject | Rings and Algebras | |
| dc.subject | Operator Algebras | |
| dc.subject | Primary 16D70, 46L35; Secondary 06A12, 06F05, 46L80 | |
| dc.title | Nonstable $K$-theory for graph algebras | |
| dc.type | text |