C*‐Algèbres De Kac Et Algèbres De Kac

S. Baaj and G. Skandalis have proved that, to every Kac algebra, as studied by J.‐M. Schwartz and the first author, corresponds a canonical C*‐Kac algebra, as studied by the second author. This article proves the converse result. So, we have then a complete proof that the C* version and the von Neumann version of this theory are exactly equivalent, as are, in the commutative case, thanks to A. Weil's theorem, locally compact groups and measured groups with a left‐invariant measure.