G. Elliott extended the classification theory of -algebras to certain real rank zero inductive limits of subhomogeneous -algebras with one dimensional spectrum. We show that this class of -algebras is not closed under extensions. The relevant obstruction is related to the torsion subgroup of the -group. Perturbation and lifting results are provided for certain subhomogeneous -algebras.
G. Elliott a généralisé la théorie de la classification des -algèbres à une classe de -algèbres de rang réel zéro qui sont limites inductives de -algèbres subhomogènes. On montre que cette classe de -algèbres n’est pas fermée pour l’extension. On a une obstruction qui est reliée à la partie de torsion du groupe . On obtient des résultats de perturbation et de relèvement pour des -algèbres subhomogènes.
@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}, mrnumber = {96b:46075}, zbl = {0814.46044}, language = {en}, url = {http://archive.numdam.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 - http://archive.numdam.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 http://archive.numdam.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, Volume 44 (1994) no. 3, pp. 907-925. doi : 10.5802/aif.1420. http://archive.numdam.org/articles/10.5802/aif.1420/
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