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A Continuous Field of Projectionless C*-Algebras

Published online by Cambridge University Press:  20 November 2018

Andrew Dean
Andrew Dean*
Affiliation:
Department of Mathematical Sciences, Lakehead University, 955 Oliver Road, Thunder Bay, Ontario, P7B 5E1. email: adean@mercury.lakeheadu.ca
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Abstract

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We use some results about stable relations to show that some of the simple, stable, projectionless crossed products of ${{O}_{2}}$ by $\mathbb{R}$ considered by Kishimoto and Kumjian are inductive limits of type I ${{C}^{*}}$-algebras. The type I ${{C}^{*}}$-algebras that arise are pullbacks of finite direct sums of matrix algebras over the continuous functions on the unit interval by finite dimensional ${{C}^{*}}$-algebras.

Keywords

46L3546L57
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 53 , Issue 1 , 01 February 2001 , pp. 51 - 72
Copyright
Copyright © Canadian Mathematical Society 2001

References

[Bl] Blackadar, B., K-theory for operator algebras. Math. Sci. Res. Inst. Publ. 5, Springer-Verlag, Berlin-New York, 1986.Google Scholar
[Co] Connes, A., An analogue of the Thom isomorphism for crossed products of a C*-algebra by an action of R. Adv. Math. 39(1981), 31–55.Google Scholar
[Cu] Cuntz, J., K-theory for certain C*-algebras. Ann. of Math. (2) 113(1981), 181–197.Google Scholar
[Dix] Dixmier, J., C*-algebras. North Holland, Amsterdam-New York-Oxford, 1977.Google Scholar
[ELP] Eilers, S., Loring, T. and Pedersen, G., Stability of anti-commutation relations: An application of non-commutative CW-complexes. J. Reine Angew.Math, to appear.Google Scholar
[E1] Elliott, G. A., The classification problem for amenable C*-algebras. Proc. ICM (Zurich, 1994), Vol. 1, 2, Birkhauser, Basel, 1995, 922–932.Google Scholar
[E2] Elliott, G. A., An invariant for simple C*-algebras. Invited Papers/Articles Sollicités (eds. Carrell, J. B. and Murty, R.), Canadian Mathematical Society, Ottawa, 1996, 61–90.Google Scholar
[ENN] Elliott, G. A., Natsume, T. and Nest, R., The Heisenberg group and K-Theory. K-Theory 7(1993), 409–428.Google Scholar
[Ev] Evans, D. E., On On. Publ. Res. Inst.Math. Sci. 16(1980), 915–927.Google Scholar
[Ks] Kishimoto, A., Simple crossed products by locally compact abelian groups. Yokohama Math. J. 28(1980), 69–85.Google Scholar
[KK1] Kishimoto, A. and Kumjian, A., Simple, stably projectionless C*-algebras arising as crossed products. Canad. J. Math. (5) 48(1996), 980–996.Google Scholar
[KK2] Kishimoto, A. and Kumjian, A., Crossed products of Cuntz algebras by quasi-free automorphisms. Fields Inst. Commun. 13(1997), 173–192.Google Scholar
[L] Loring, T., Lifting solutions to perturbing problems in C*-algebras. Fields InstituteMonographs 8, Amer. Math. Soc., Providence, RI, 1997.Google Scholar
[OP] Olesen, D. and Pedersen, G., Partially inner C*-dynamical systems. J. Funct. Anal. 66(1986), 262–281.Google Scholar
[Ped] Pedersen, G. K., C*-algebras and their automorphism groups. Academic Press, London-New York-San Francisco, 1979.Google Scholar
[Rie] Rieffel, M., Continuous fields of C*-algebras coming from group cocycles and actions. Math. Ann. 283(1989), 631–643.Google Scholar
[Rør] Rørdam, M., Classification of certain infinite simple C*-algebras. J. Funct. Anal. 131(1995).Google Scholar