no. 3
Stabilité des C * -algèbres de feuilletages
Annales de l'Institut Fourier, Volume 33 (1983) no. 3, pp. 201-208.

Let A be either the reduced or the maximal C * -algebra associated to a foliated manifold V,F, and let K be the elementary C * -algebra of compact operators. Then, it dimF≠0, it is shown that A is isomorphic to the tensor product A⊗K.

Soit A la C * -algèbre, ou bien réduite ou bien maximale, associée à la variété feuilletée (V,F), et K la C * -algèbre élémentaire des opérateurs compacts. Alors, si dimF≠0, on montre que A est isomorphe à A⊗K.

@article{AIF_1983__33_3_201_0,
     author = {Hilsum, Michel and Skandalis, Georges},
     title = {Stabilit\'e des $C^*$-alg\`ebres de feuilletages},
     journal = {Annales de l'Institut Fourier},
     pages = {201--208},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {33},
     number = {3},
     year = {1983},
     doi = {10.5802/aif.936},
     zbl = {0505.46043},
     mrnumber = {85f:58115},
     language = {fr},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.936/}
}
TY  - JOUR
AU  - Hilsum, Michel
AU  - Skandalis, Georges
TI  - Stabilité des $C^*$-algèbres de feuilletages
JO  - Annales de l'Institut Fourier
PY  - 1983
SP  - 201
EP  - 208
VL  - 33
IS  - 3
PB  - Institut Fourier
PP  - Grenoble
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.936/
UR  - https://zbmath.org/?q=an%3A0505.46043
UR  - https://www.ams.org/mathscinet-getitem?mr=85f:58115
UR  - https://doi.org/10.5802/aif.936
DO  - 10.5802/aif.936
LA  - fr
ID  - AIF_1983__33_3_201_0
ER  - 
%0 Journal Article
%A Hilsum, Michel
%A Skandalis, Georges
%T Stabilité des $C^*$-algèbres de feuilletages
%J Annales de l'Institut Fourier
%D 1983
%P 201-208
%V 33
%N 3
%I Institut Fourier
%C Grenoble
%U https://doi.org/10.5802/aif.936
%R 10.5802/aif.936
%G fr
%F AIF_1983__33_3_201_0
Hilsum, Michel; Skandalis, Georges. Stabilité des $C^*$-algèbres de feuilletages. Annales de l'Institut Fourier, Volume 33 (1983) no. 3, pp. 201-208. doi : 10.5802/aif.936. https://aif.centre-mersenne.org/articles/10.5802/aif.936/

[1] A. Connes, Sur la théorie non commutative de l'intégration, Lect. Notes in Math., n° 725, Springer (1979), 19 à 143. | MR | Zbl

[2] A. Connes, Survey of foliations and operator algebras, Operator algebras and applications, Proc. of Symp. in Pure Math., vol 38, part 1, A.M.S., Providence 1982. | Zbl

[3] A. Connes, G. Skandalis, The longitudinal index theorem for foliations, Preprint I.H.E.S./M/82/24. | Zbl

[4] G.G. Kasparov, Hilbert C*-modules, Theorems of Stinespring and Voiculescu, Journal of Operator Theory, vol. 4 n° 1 (1980). | MR | Zbl

[5] J.F. Plante, Foliations with measure preserving holonomy, Ann. of Math., 102 (1975). | MR | Zbl

[6] J.N. Renault, A groupoid approach to C*-algebras, Lect. Notes in Math., n° 793, Springer (1980). | MR | Zbl

[7] M. Rieffel, Morita equivalence for C* and W* algebras, Journal of Pure and Applied Algebra, 5 (1974). | MR | Zbl

Cited by Sources: