A Characterization of Depth 2 Subfactors of II1 Factors

We characterize finite index depth 2 inclusions of type II1 factors in terms of actions of weak Kac algebras and weak C*-Hopf algebras. If N⊂M⊂M1⊂M2⊂… is the Jones tower constructed from such an inclusion N⊂M, then B=M′∩M2 has a natural structure of a weak C*-Hopf algebra and there is a minimal action of B on M1 such that M is the fixed point subalgebra of M1 and M2 is isomorphic to the crossed product of M1 and B. This extends the well-known results for irreducible depth 2 inclusions.