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K-Homology of the Rotation Algebras Aθ

Published online by Cambridge University Press:  20 November 2018

Tom Hadfield
Tom Hadfield*
Affiliation:
School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS, U.K. e-mail: [email protected]
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Abstract

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We study the $\text{K}$-homology of the rotation algebras ${{A}_{\theta }}$ using the six-term cyclic sequence for the $\text{K}$-homology of a crossed product by $Z$. In the case that $\theta $ is irrational, we use Pimsner and Voiculescu's work on $\text{AF}$-embeddings of the ${{A}_{\theta }}$ to search for the missing generator of the even $\text{K}$-homology.

Keywords

58B3419K3346L
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 56 , Issue 5 , 01 October 2004 , pp. 926 - 944
Copyright
Copyright © Canadian Mathematical Society 2004

References

[1] Baum, P., Connes, A. and Higson, N.. Classifying space for proper actions and K-theory of group C*-algebras. Contemp.Math. 167(1994), 241–291.Google Scholar
[2] Blackadar, B., K-theory for operator algebras. Mathematical Sciences Research Institute Publications, 5, Cambridge University Press, Cambridge, 1998.Google Scholar
[3] Connes, A., Noncommutative geometry. Academic Press, San Diego, 1994.Google Scholar
[4] Davidson, K., C*-algebras by example. Fields InstituteMonographs, 6, Amer. Math. Soc., Providence, RI, 1996.Google Scholar
[5] Pimsner, M. and Voiculescu, D.-V., Exact sequences for K-groups and Ext groups of certain cross-product algebras. J. Operator Theory 4(1980), 93–118.Google Scholar
[6] Pimsner, M. and Voiculescu, D.-V., Imbedding the irrational rotation algebras into an AF-algebra. J. Operator Theory 4(1980), 201–220.Google Scholar
[7] Popa, S. and Rieffel, M.. The Ext groups of the C*-algebras associated with irrational rotations. J. Operator Theory 3(1980), 271–274 .Google Scholar
[8] Rieffel, M., C*-algebras associated with irrational rotations. Pacific J. Math. 93(1981), 415–429.Google Scholar
[9] Rieffel, M., Noncommutative tori—a case study of noncommutative differentiable manifolds. Contemp. Math 105(1990), 191–211.Google Scholar
[10] Rosenberg, J. and Schochet, C., The Kunneth theorem and the universal coefficient theorem for Kasparov's generalised K-functor. Duke Math. J. 55(1987), 431–474.Google Scholar
[11] Weibel, C., An introduction to homological algebra. Cambridge Studies in AdvancedMathematics, 38, Cambridge University Press, Cambridge, 1994.Google Scholar