A characterization of depth 2 subfactors of II_1 factors

Details A characterization of depth 2 subfactors of II_1 factors A characterization of depth 2 subfactors of II_1 factors

1998-10-06

arxiv.org/abs/math/9810028v2

J. Func. Analysis, 171 (2000), no.2, 278-307

Mathematics

Quantum Algebra

Latex, 26 pages, more precise statements of Theorems 4.17 and 5.7 given, several minor errors corrected

Scientific paper

We characterize finite index depth 2 inclusions of type II_1 factors in terms of actions of weak Kac algebras and weak C*-Hopf algebras. If N\subset M \subset M_1 \subset M_2 \subset ... is the Jones tower constructed from such an inclusion N\subset M, then B=M^\prime \cap M_2 has a natural structure of a weak C*-Hopf algebra and there is a minimal action of B on M_1 such that M is the fixed point subalgebra of M_1, and M_2 is isomorphic to the crossed product of M_1 and B. This extends the well-known results for irreducible depth 2 inclusions.

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