The Noncommutative Geometry of Graph $C^*$-Algebras I: The Index Theorem
| dc.creator | Pask, David | |
| dc.creator | Rennie, Adam | |
| dc.date | 2005-08-01 | |
| dc.date.accessioned | 2026-07-07T05:22:08Z | |
| dc.date.available | 2026-07-07T05:22:08Z | |
| dc.description | We investigate conditions on a graph $C^*$-algebra for the existence of a faithful semifinite trace. Using such a trace and the natural gauge action of the circle on the graph algebra, we construct a smooth $(1,\infty)$-summable semfinite spectral triple. The local index theorem allows us to compute the pairing with $K$-theory. This produces invariants in the $K$-theory of the fixed point algebra, and these are invariants for a finer structure than the isomorphism class of $C^*(E)$. | |
| dc.description | 33 pages | |
| dc.identifier | https://arxiv.org/abs/math/0508025 | |
| dc.identifier | http://arxiv.org/abs/math/0508025 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75944 | |
| dc.subject | Functional Analysis | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L80; 58B34 | |
| dc.title | The Noncommutative Geometry of Graph $C^*$-Algebras I: The Index Theorem | |
| dc.type | text |