Stabilité des $C^{*}$-algèbres de feuilletages

Hilsum, Michel; Skandalis, Georges

Annales de l'Institut Fourier, Tome 33 (1983) no. 3, pp. 201-208

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 $A\otimes K$.

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$F\ne 0$, it is shown that $A$ is isomorphic to the tensor product $A\otimes K$.

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