Inclusions irréductibles de facteurs et unitaires multiplicatifs, II

Résumé n irreducible depth 2 inclusionM0⊂M1of factors with a faithful semifinite normal operator-valued weight, verifying a regularity condition, we construct the canonical tower (Mi)i∈N. We prove then that both relative commutantsM2∩M′0andM3∩M′1bear Woronowicz algebra structures, dual to each other, as defined by Masuda and Nakagami. Moreover, there exists an outer action ofM3∩M′1onM1, such thatM0is the fixed-point algebra andM2is the crossed-product. The tower appears then as the tower of successive crossed-products.