THE NONCOMMUTATIVE GEOMETRY OF k-GRAPH C∗-ALGEBRAS
نویسندگان
چکیده
This paper is comprised of two related parts. First we discuss which k-graph algebras have faithful traces. We characterise the existence of a faithful semifinite lowersemicontinuous gauge-invariant trace on C∗(Λ) in terms of the existence of a faithful graph trace on Λ. Second, for k-graphs with faithful gauge invariant trace, we construct a smooth (k,∞)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 action. As with graph algebras, the index pairing is an invariant for a finer structure than the isomorphism class of the algebra.
منابع مشابه
Noncommutative Manifolds from Graph and K-graph C * -algebras
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