# 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} }

## References

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### FREDHOLM MODULES OVER GRAPH $C^{\ast }$-ALGEBRAS

- MathematicsBulletin of the Australian Mathematical Society
- 2015

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…

### ON Z/2Z-GRADED KK-THEORY AND ITS RELATION WITH THE GRADED Ext-FUNCTOR

- Mathematics
- 1999

This paper studies the relation between KK-theory and the Ext- functor of Kasparov for Z2-graded C -algebras. We use an approach similar to the picture of J. Cuntz in the ungraded case. We show that…

### Cuntz-Krieger Algebras of Infinite Graphs and Matrices

- Mathematics
- 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…

### The ideal structure of the $C\sp *$-algebras of infinite graphs

- Mathematics
- 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…

### Bimodules for Cuntz-Krieger algebras of infinite matrices

- MathematicsBulletin 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…

### The K-theory of Cuntz-Krieger algebras for infinite matrices

- 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.

### On the K-theory of Cuntz-Krieger algebras

- Mathematics
- 1996

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…

### Morita Equivalence and Continuous-Trace $C^*$-Algebras

- Mathematics
- 1998

The algebra of compact operators Hilbert $C^*$-modules Morita equivalence Sheaves, cohomology, and bundles Continuous-trace $C^*$-algebras Applications Epilogue: The Brauer group and group actions…