Geodesic
A Continuous Field of Projectionless C *-Algebras
Canadian journal of mathematics, Tome 53 (2001) no. 1, pp. 51-72

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CJM-2001-003-2
Mots-clés : 46L35, 46L57 
Dean, Andrew. A Continuous Field of Projectionless C *-Algebras. Canadian journal of mathematics, Tome 53 (2001) no. 1, pp. 51-72. doi: 10.4153/CJM-2001-003-2
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[Bl] [Bl] Blackadar, B., K-theory for operator algebras. Math. Sci. Res. Inst. Publ. 5, Springer-Verlag, Berlin-New York, 1986. Google Scholar

[Co] [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] [Cu] Cuntz, J., K-theory for certain C*-algebras. Ann. of Math. (2) 113(1981), 181–197. Google Scholar

[Dix] [Dix] Dixmier, J., C*-algebras. North Holland, Amsterdam-New York-Oxford, 1977. Google Scholar

[ELP] [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] [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] [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] [ENN] Elliott, G. A., Natsume, T. and Nest, R., The Heisenberg group and K-Theory. K-Theory 7(1993), 409–428. Google Scholar

[Ev] [Ev] Evans, D. E., On On. Publ. Res. Inst.Math. Sci. 16(1980), 915–927. Google Scholar

[Ks] [Ks] Kishimoto, A., Simple crossed products by locally compact abelian groups. Yokohama Math. J. 28(1980), 69–85. Google Scholar

[KK1] [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] [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] [L] Loring, T., Lifting solutions to perturbing problems in C*-algebras. Fields InstituteMonographs 8, Amer. Math. Soc., Providence, RI, 1997. Google Scholar

[OP] [OP] Olesen, D. and Pedersen, G., Partially inner C*-dynamical systems. J. Funct. Anal. 66(1986), 262–281. Google Scholar

[Ped] [Ped] Pedersen, G. K., C*-algebras and their automorphism groups. Academic Press, London-New York-San Francisco, 1979. Google Scholar

[Rie] [Rie] Rieffel, M., Continuous fields of C*-algebras coming from group cocycles and actions. Math. Ann. 283(1989), 631–643. Google Scholar

[Rør] [Rør] Rørdam, M., Classification of certain infinite simple C*-algebras. J. Funct. Anal. 131(1995). Google Scholar

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