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

25 May 2020  ·  Quinn Patterson, Adam Sierakowski, Aidan Sims, Jonathan Taylor ·

We establish exact sequences in $KK$-theory for graded relative Cuntz-Pimsner algebras associated to nondegenerate $C^*$-correspondences. We use this to calculate the graded $K$-theory and $K$-homology of relative Cuntz-Krieger algebras of directed graphs for gradings induced by $\{0,1\}$-valued labellings of their edge sets...

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Operator Algebras K-Theory and Homology 46L05, 19K35