The Noncommutative Geometry of Graph C*-Algebras I: The Index Theorem
David Pask, Adam Rennie
Abstract
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 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).
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