Stabilité des C * -algèbres de feuilletages

Michel Hilsum; Georges Skandalis

Annales de l'institut Fourier (1983)

  • Volume: 33, Issue: 3, page 201-208
  • ISSN: 0373-0956

Abstract

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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 dim F ≠ 0 , it is shown that A is isomorphic to the tensor product A ⊗ K .

How to cite

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Hilsum, Michel, and Skandalis, Georges. "Stabilité des $C^*$-algèbres de feuilletages." Annales de l'institut Fourier 33.3 (1983): 201-208. <http://eudml.org/doc/74596>.

@article{Hilsum1983,
abstract = {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 dim$\, F\ne 0$, on montre que $A$ est isomorphe à $A\otimes K$.},
author = {Hilsum, Michel, Skandalis, Georges},
journal = {Annales de l'institut Fourier},
keywords = {foliation; reduced or maximal C*-algebra},
language = {fre},
number = {3},
pages = {201-208},
publisher = {Association des Annales de l'Institut Fourier},
title = {Stabilité des $C^*$-algèbres de feuilletages},
url = {http://eudml.org/doc/74596},
volume = {33},
year = {1983},
}

TY - JOUR
AU - Hilsum, Michel
AU - Skandalis, Georges
TI - Stabilité des $C^*$-algèbres de feuilletages
JO - Annales de l'institut Fourier
PY - 1983
PB - Association des Annales de l'Institut Fourier
VL - 33
IS - 3
SP - 201
EP - 208
AB - 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 dim$\, F\ne 0$, on montre que $A$ est isomorphe à $A\otimes K$.
LA - fre
KW - foliation; reduced or maximal C*-algebra
UR - http://eudml.org/doc/74596
ER -

References

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  1. [1] A. CONNES, Sur la théorie non commutative de l'intégration, Lect. Notes in Math., n° 725, Springer (1979), 19 à 143. Zbl0412.46053MR81g:46090
  2. [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. Zbl0531.57023
  3. [3] A. CONNES, G. SKANDALIS, The longitudinal index theorem for foliations, Preprint I.H.E.S./M/82/24. Zbl0575.58030
  4. [4] G.G. KASPAROV, Hilbert C*-modules, Theorems of Stinespring and Voiculescu, Journal of Operator Theory, vol. 4 n° 1 (1980). Zbl0456.46059MR82b:46074
  5. [5] J.F. PLANTE, Foliations with measure preserving holonomy, Ann. of Math., 102 (1975). Zbl0314.57018MR52 #11947
  6. [6] J.N. RENAULT, A groupoid approach to C*-algebras, Lect. Notes in Math., n° 793, Springer (1980). Zbl0433.46049MR82h:46075
  7. [7] M. RIEFFEL, Morita equivalence for C* and W* algebras, Journal of Pure and Applied Algebra, 5 (1974). Zbl0295.46099MR51 #3912

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