The Noncommutative Geometry of k-graph C*-Algebras
| dc.creator | Pask, David | |
| dc.creator | Rennie, Adam | |
| dc.creator | Sims, Aidan | |
| dc.date | 2005-12-19 | |
| dc.date | 2007-01-17 | |
| dc.date.accessioned | 2026-07-07T07:41:16Z | |
| dc.date.available | 2026-07-07T07:41:16Z | |
| dc.description | This paper is comprised of two related parts. First we discuss which k-graph algebras have faithful gauge invariant traces, where the gauge action of $\T^k$ is the canonical one. We give a sufficient condition for the existence of such a trace, identify the C*-algebras of k-graphs satisfying this condition up to Morita equivalence, and compute their K-theory. For k-graphs with faithful gauge invariant trace, we construct a smooth $(k,\infty)$-summable semifinite spectral triple. We use the semifinite local index theorem to compute the pairing with K-theory. This numerical pairing can be obtained by applying the trace to a KK-pairing with values in the K-theory of the fixed point algebra of the $\T^k$ action. As with graph algebras, the index pairing is an invariant for a finer structure than the isomorphism class of the algebra. | |
| dc.description | 38 pages, some pictures drawn in picTeX Some minor technical revisions. Material has been reorganised with detailed discussion of k-graphs admitting graph traces shortened and moved to an appendix. This version to appear in K-theory | |
| dc.identifier | https://arxiv.org/abs/math/0512438 | |
| dc.identifier | http://arxiv.org/abs/math/0512438 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/122042 | |
| dc.subject | Operator Algebras | |
| dc.subject | K-Theory and Homology | |
| dc.subject | 46L05 | |
| dc.title | The Noncommutative Geometry of k-graph C*-Algebras | |
| dc.type | text |