Stabilité des C * -algèbres de feuilletages
Hilsum, Michel ; Skandalis, Georges
Annales de l'Institut Fourier, Tome 33 (1983), p. 201-208 / Harvested from Numdam
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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.

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.

@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},
     volume = {33},
     year = {1983},
     pages = {201-208},
     doi = {10.5802/aif.936},
     mrnumber = {85f:58115},
     zbl = {0505.46043},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/AIF_1983__33_3_201_0}
}

Hilsum, Michel; Skandalis, Georges. Stabilité des $C^*$-algèbres de feuilletages. Annales de l'Institut Fourier, Tome 33 (1983) pp. 201-208. doi : 10.5802/aif.936. http://gdmltest.u-ga.fr/item/AIF_1983__33_3_201_0/

[1] A. Connes, Sur la théorie non commutative de l'intégration, Lect. Notes in Math., n° 725, Springer (1979), 19 à 143. | MR 81g:46090 | Zbl 0412.46053

[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 0531.57023

[3] A. Connes, G. Skandalis, The longitudinal index theorem for foliations, Preprint I.H.E.S./M/82/24. | Zbl 0575.58030

[4] G.G. Kasparov, Hilbert C*-modules, Theorems of Stinespring and Voiculescu, Journal of Operator Theory, vol. 4 n° 1 (1980). | MR 82b:46074 | Zbl 0456.46059

[5] J.F. Plante, Foliations with measure preserving holonomy, Ann. of Math., 102 (1975). | MR 52 #11947 | Zbl 0314.57018

[6] J.N. Renault, A groupoid approach to C*-algebras, Lect. Notes in Math., n° 793, Springer (1980). | MR 82h:46075 | Zbl 0433.46049

[7] M. Rieffel, Morita equivalence for C* and W* algebras, Journal of Pure and Applied Algebra, 5 (1974). | MR 51 #3912 | Zbl 0295.46099