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A Characterization of Depth 2 Subfactors of II1 Factors

✍ Scribed by Dmitri Nikshych; Leonid Vainerman

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
261 KB
Volume
171
Category
Article
ISSN
0022-1236

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✦ Synopsis

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/M/M 1 / M 2 / } } } is the Jones tower constructed from such an inclusion N/M, then B= M$ & 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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