Fredholm Modules over Graph C∗-Algebras

Tyrone Crisp

doi:10.1017/S0004972715000556

Fredholm Modules over Graph C^∗-Algebras

Tyrone Crisp^*

^*Corresponding author for this work

Department of Mathematical Sciences

1 Citation (Scopus)

Abstract

We present two applications of explicit formulas, due to Cuntz and Krieger, for computations in K-homology of graph C^∗-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.

Original language	English
Journal	Bulletin of the Australian Mathematical Society
Volume	92
Issue number	2
Pages (from-to)	302-315
Number of pages	14
ISSN	0004-9727
DOIs	https://doi.org/10.1017/S0004972715000556
Publication status	Published - 2 Sept 2015

Keywords

graph C∗-algebras
K-homology

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10.1017/S0004972715000556

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title = "Fredholm Modules over Graph C∗-Algebras",

abstract = "We present two applications of explicit formulas, due to Cuntz and Krieger, for computations in K-homology of graph C∗-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.",

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N2 - We present two applications of explicit formulas, due to Cuntz and Krieger, for computations in K-homology of graph C∗-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.

AB - We present two applications of explicit formulas, due to Cuntz and Krieger, for computations in K-homology of graph C∗-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.

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KW - K-homology

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DO - 10.1017/S0004972715000556

M3 - Journal article

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SP - 302

EP - 315

JO - Bulletin of the Australian Mathematical Society

JF - Bulletin of the Australian Mathematical Society

IS - 2

ER -

Fredholm Modules over Graph C^∗-Algebras

Abstract

Keywords

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