Groupoïdes Quantiques Finis

Résumé A notion of pseudo-multiplicative unitaries appeared, first with a commutative basis in the study of measured groupoids and then in a more general case in depth-2 inclusions of von Neumann algebras. This article studies the finite dimensional version of this formalism generalizing S. Baaj and G. Skandalisʹ works to (finite dimensional) quantum groupoids. Other works by T. Yamanouchi and more recently by G. Bohm, K. Szlachányi, and F. Nill or by L. Vainerman and D. Nikshych, enter into that theory.