A characterization of depth 2 subfactors of II1 factors
D. Nikshych, L. Vainerman
Abstract
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.
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