Abstract
For actions on arbitrary inclusions of factors with finite index, we define an algebraic property called "strong freeness". In the case of strongly amenable subfactors of type II∞ or IIIλ (0 < λ < 1), this property is shown to be a characterization of centrally free actions. We then classify strongly free actions of discrete amenable groups on strongly amenable subfactors of type II∞, and strongly free actions of a class of discrete amenable groups (which include ℤn, n ∈ ℕ) on strongly amenable subfactors of type IIIλ. Namely, we show that the (generalized) fundamental homomorphism is a complete invariant for cocycle conjugacy in both cases.
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