## $$C^*$$-algèbres de Kac et algèbres de Kac.(French)Zbl 0792.46040

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, in the commutative case, are equivalent, thanks to A. Weil’s theorem, locally compact groups and measured groups with a left- invariant measure.
Reviewer: M.Enock (Paris)

### MSC:

 46L05 General theory of $$C^*$$-algebras 22D25 $$C^*$$-algebras and $$W^*$$-algebras in relation to group representations 46L51 Noncommutative measure and integration 46L53 Noncommutative probability and statistics 46L54 Free probability and free operator algebras 47L50 Dual spaces of operator algebras 22D35 Duality theorems for locally compact groups

### Keywords:

Kac algebra; $$C^*$$-Kac algebra
Full Text: