# Graded K-theory and K-homology of relative Cuntz–Pimsner algebras and graph C⁎-algebras

```@article{Patterson2020GradedKA,
title={Graded K-theory and K-homology of relative Cuntz–Pimsner algebras and graph C⁎-algebras},
author={Quinn Patterson and Adam Sierakowski and Aidan Sims and Jonathan Taylor},
journal={Journal of Mathematical Analysis and Applications},
year={2020},
volume={496},
pages={124822}
}```
• Published 25 May 2020
• Mathematics
• Journal of Mathematical Analysis and Applications

## References

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We present two applications of explicit formulas, due to Cuntz and Krieger, for computations in \$K\$-homology of graph \$C^{\ast }\$-algebras. We prove that every \$K\$-homology class for such an algebra
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• 2003
We show that the Cuntz-Krieger algebras of infinite graphs and infinite {0,1}-matrices can be approximated by those of finite graphs. We then use these approximations to deduce the main uniqueness
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• 2001
We classify the gauge-invariant ideals in the C*-algebras of infinite directed graphs, and describe the quotients as graph algebras. We then use these results to identify the gauge-invariant
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• Mathematics
Bulletin of the Australian Mathematical Society
• 2000
We show that any Cuntz-Krieger algebra A over an infinite 0–1 matrix A may be realised as a Cuntz-Pimsner algebra X for a Hilbert bimodule X over a suitable Abelian C*-algebra with totally
• Mathematics
• 1998
We compute the K-theory groups of the Cuntz-Krieger C -algebra OA associ- ated to an infinite matrix A of zeros and ones.
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We extend the uniqueness and simplicity results of Cuntz and Krieger to the countably infinite case, under a row-finite condition on the matrix A. Then we present a new approach to calculating the
• Mathematics
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