The noncommutative geometry of graph C*-algebras I: The index theorem

By David Pask, A. Rennie. 2005

84 citations recorded by the source corpus.

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,∞)-summable semi-finite 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).

Subfields: Algebra and Number Theory, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/29fd49d4775141de0525fbaf2e1ba8a3b850d24f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. A. Rennie
2. David Pask
3. Alan L. Carey
4. Fedor Sukochev
5. Aidan Sims
6. V. Gayral
7. Trent Yeend
8. Iain Raeburn

In Mathematical Physics

1. A. Rennie
2. David Pask
3. Alan L. Carey
4. Fedor Sukochev
5. Aidan Sims
6. V. Gayral
7. Trent Yeend
8. Iain Raeburn

In Statistical and Nonlinear Physics

1. Alan L. Carey
2. Fedor Sukochev
3. V. Gayral
4. Aidan Sims
5. A. Rennie
6. David Pask

Citations in the corpus

• The Noncommutative Geometry of k-graph C*-Algebras (2005, methodology): “ory. The pay-off for noncommutative geometry is that our analysis allows us to construct infinitely many examples of (semifinite) spectral triples of every integer dimension k ≥ 1 (k = 1 is contained in [PRen]). These spectral triples are generically semifinite, and so come from KK classes rather than K”
• Index Theory for Locally Compact Noncommutative Geometries (2011, methodology): “Applications of this formula to graph and k-graph algebras appear in [42,43].”
• The Dixmier trace and asymptotics of zeta functions (2006, unknown): “Numerous other noncommutative spaces which are (p,∞)-summable have been studied, [7, 8, 9, 17, 19, 35, 36], some with physical applications or relevance.”