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

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  19 June 2015

TYRONE CRISP
TYRONE CRISP*
Affiliation:
Department of Mathematical Sciences, Universitetsparken 5, 2100 Copenhagen Ø, Denmark email crisp@math.ku.dk
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Abstract

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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 is represented by a Fredholm module having finite-rank commutators, and we exhibit generating Fredholm modules for the $K$-homology of quantum lens spaces.

Keywords

K-homologygraph C∗ -algebras

MSC classification

Primary: 46L80: $K$-theory and operator algebras (including cyclic theory)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 92 , Issue 2 , October 2015 , pp. 302 - 315
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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