The Noncommutative Geometry of k-graph C*-Algebras

Details The Noncommutative Geometry of k-graph C*-Algebras The Noncommutative Geometry of k-graph C*-Algebras

2005-12-19

arxiv.org/abs/math/0512438v2

Mathematics

Operator Algebras

38 pages, some pictures drawn in picTeX Some minor technical revisions. Material has been reorganised with detailed discussion

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

The Noncommutative Geometry of k-graph C*-Algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Noncommutative Geometry of k-graph C*-Algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Noncommutative Geometry of k-graph C*-Algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-281516