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arXiv · 2005.11921

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

Quinn Patterson·Adam Sierakowski·Aidan Sims·Jonathan Taylor
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Abstract

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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Quinn Patterson, Adam Sierakowski, Aidan Sims, Jonathan Taylor. 2020-05-25. Graded $K$-theory and $K$-homology of relative Cuntz-Pimsner algebras and graph $C^*$-algebras. https://doi.org/10.1016/j.jmaa.2020.124822

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