no. 3
Extensions of certain real rank zero C * -algebras
Annales de l'Institut Fourier, Tome 44 (1994) no. 3, pp. 907-925.

G. Elliott a généralisé la théorie de la classification des AF-algèbres à une classe de C * -algèbres de rang réel zéro qui sont limites inductives de C * -algèbres subhomogènes. On montre que cette classe de C * -algèbres n’est pas fermée pour l’extension. On a une obstruction qui est reliée à la partie de torsion du groupe K 1 . On obtient des résultats de perturbation et de relèvement pour des C * -algèbres subhomogènes.

G. Elliott extended the classification theory of AF-algebras to certain real rank zero inductive limits of subhomogeneous C * -algebras with one dimensional spectrum. We show that this class of C * -algebras is not closed under extensions. The relevant obstruction is related to the torsion subgroup of the K 1 -group. Perturbation and lifting results are provided for certain subhomogeneous C * -algebras.

@article{AIF_1994__44_3_907_0,
     author = {Dadarlat, Marius and Loring, Terry A.},
     title = {Extensions of certain real rank zero $C^*$-algebras},
     journal = {Annales de l'Institut Fourier},
     pages = {907--925},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {44},
     number = {3},
     year = {1994},
     doi = {10.5802/aif.1420},
     zbl = {0814.46044},
     mrnumber = {96b:46075},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1420/}
}
TY  - JOUR
AU  - Dadarlat, Marius
AU  - Loring, Terry A.
TI  - Extensions of certain real rank zero $C^*$-algebras
JO  - Annales de l'Institut Fourier
PY  - 1994
SP  - 907
EP  - 925
VL  - 44
IS  - 3
PB  - Association des Annales de l’institut Fourier
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.1420/
DO  - 10.5802/aif.1420
LA  - en
ID  - AIF_1994__44_3_907_0
ER  - 
%0 Journal Article
%A Dadarlat, Marius
%A Loring, Terry A.
%T Extensions of certain real rank zero $C^*$-algebras
%J Annales de l'Institut Fourier
%D 1994
%P 907-925
%V 44
%N 3
%I Association des Annales de l’institut Fourier
%U https://aif.centre-mersenne.org/articles/10.5802/aif.1420/
%R 10.5802/aif.1420
%G en
%F AIF_1994__44_3_907_0
Dadarlat, Marius; Loring, Terry A. Extensions of certain real rank zero $C^*$-algebras. Annales de l'Institut Fourier, Tome 44 (1994) no. 3, pp. 907-925. doi : 10.5802/aif.1420. https://aif.centre-mersenne.org/articles/10.5802/aif.1420/

[Bl] B. Blackadar, K-theory for Operator Algebras, M.S.R.I. Monographs No. 5, Springer-Verlag, Berlin and New York (1986). | MR | Zbl

[Br1] L. G. Brown, Extensions of AF algebras : The projection lifting problem, Proc. Sympos. Pure Math., vol. 38, Amer. Math. Soc., Providence, R.I., 1982. | Zbl

[Br2] L. G. Brown, The Universal coefficient theorem for Ext and quasidiagonality, Operator Algebras and Group Representations, vol. 17, Pitman Press, Boston, London and Melbourne, (1983), 60-64. | MR | Zbl

[BP] L. G. Brown and G. K. Pedersen, C*-algebras of real rank zero, J. Funct. Anal., vol. 99 (1991), 131-149. | MR | Zbl

[BD] L. G. Brown and M. Dadarlat, Extensions of C*-algebras and quasidiagonality, preprint (1993). | Zbl

[CH] A. Connes and N. Higson, Déformations, morphismes asymptotiques et K-théorie bivariante, C.R. Acad. Sci. Paris, vol. 313 (1990), 101-106. | MR | Zbl

[DL1] M. Dadarlat and T. A. Loring, The K-theory of abelian subalgebras of AF algebras, J. reine angew. Math., 432 (1992), 39-55. | EuDML | MR | Zbl

[DL2] M. Dadarlat and T. A. Loring, K-homology, asymptotic representations and unsuspended E-theory, to appear in J. Funct. Anal. | Zbl

[DL3] M. Dadarlat and T. A. Loring, Deformations of topological spaces predicted by E-theory, to appear in Proceedings of GPOTS, Iowa, (1993). | Zbl

[Eff] E. G. Effros, Dimensions and C*-algebras, CBMS Regional Conf. Series in Math., vol. 46, Amer. Math. Soc., Providence R. I., (1981). | Zbl

[Ell] G. Elliott, On the classification of C*-algebras of real rank zero I, to appear. | Zbl

[EK] D. Evans and A. Kishimoto, Compact group actions on UHF-algebras obtained by folding the interval, J. Funct. Anal., vol. 98 (1991), 346-348. | MR | Zbl

[K] G. G. Kasparov, The operator K-functor and extensions of C*-algebras, Math. URSS Izv., vol. 16 (1981), 513-572. | Zbl

[Li1] H. Lin, Approximation by normal elements with finite spectrum in C*-algebras of real rank zero, Preprint, (1992).

[Li2] H. Lin, Exponential rank of C*-algebras with real rank zero and the Brown-Pedersen conjecture, Preprint, (1991).

[LR] H. Lin and M. Rørdam, Extensions of inductive limits of circle algebras, Preprint Odense Universitet, (1992). | Zbl

[Lo1] T. A. Loring, C*-algebras generated by stable relations, J. Funct. Anal., 112 (1993), 159-201. | MR | Zbl

[Lo2] T. A. Loring, Projective C*-algebras, Math. Scand., (1992) to appear. | Zbl

[Lo3] T. A. Loring, Stable relations II : corona semiprojectivity and dimension-drop C*-algebras, preprint, 1993.

[R] M. A. Rieffel, Dimension and stable rank in the K-theory of C*-algebras, Proc. London Math. Soc., 46 (1983), 301-333. | MR | Zbl

[RS] J. Rosenberg and C. Schochet, The Künneth theorem and the universal coefficient theorem for Kasparov's generalized functor, Duke Math. J., 55 (1987), 431-474. | MR | Zbl

[Sa] N. Salinas, Relative quasidiagonality and KK-theory, Houston J. of Math., 18-1 (1992), 97-116. | MR | Zbl

[Z] S. Zhang, K1-groups, quasidiagonality and interpolation by multiplier projections, Trans. Amer. Math. Soc., 325 (1991), 793-818. | Zbl

Cité par Sources :