Fredholm Modules Over Graph -Algebras

Abstract

We present two applications of explicit formulas, due to Cuntz and Krieger, for computations in K-homology of graph C * -algebras. We prove that every K-homology class for such an algebra is represented by a Fredholm module having finite-rank commutators; and we exhibit generating Fredholm modules for the K-homology of quantum lens spaces.

Graded $K$-theory and $K$-homology of relative Cuntz-Pimsner algebras and graph $C^*$-algebras

“…It is less of an automatic reaction to compute K-homology for C * -algebras, but, for example, Cuntz and Krieger computed (in [6,Theorem 5.3]) the Ext-group (that is, the odd K-homology group) of the Cuntz-Krieger algebra O A of A ∈ M n (Z + ) as the cokernel of 1 − A regarded as an endomorphism of Z n . The computation was later generalised to graph C * -algebras in [10,35] (see also [5,36]).…”