Actions of discrete amenable groups on injective factors of type IIIλ, λ≠1

Sutherland, Colin E.; Takesaki, Masamichi

doi:10.2140/pjm.1989.137.405

Cited by 63 publications

(57 citation statements)

References 14 publications

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“…In many interesting cases, this orbit turns out to consist of a single element as we will see in Section 6. This invariant can be regarded as an analogue of the modular invariant of Sutherland-Takesaki [35] and the symbol ν comes from this analogy. See Section 6 for more on this analogy.…”

Section: New Invariants -An Algebraic Approach -mentioning

confidence: 99%

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Classification of approximately inner automorphisms of subfactors

Kawahigashi¹

1997

Mathematische Annalen

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For classification of approximately inner automorphisms of subfactors, we introduce a new invariant, a higher obstruction. From an algebraic viewpoint, this can be regarded as a generalization of the Connes obstruction, and from an analytic viewpoint, this can be regarded as a generalization of the Jones invariant κ. We have two classification theorems for approximately inner automorphisms of strongly amenable subfactors with known invariants and this new one. In particular, our theorems give a complete classification of automorphisms, up to outer conjugacy, of AFD subfactors of type II 1 with index less than four except for one special case for A 4n−1 and E 6 .

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Section: New Invariants -An Algebraic Approach -mentioning

confidence: 99%

“…We then study Hecke algebra subfactors of Wenzl constructed in [37]. Finally, we discuss analogy between our classification here and the classification of automorphisms of injective type III factors in [9], [25], [35].…”

Section: Examples and Remarksmentioning

confidence: 99%

Classification of approximately inner automorphisms of subfactors

Kawahigashi¹

1997

Mathematische Annalen

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“…Here, U(R) is the semi direct product of U(R) by the extended modular action of Z 1 (F (R)) as in [14]. Except for the lower right corner H 1 (F (R)), all groups are Polish and all maps are continuous.…”

Section: Intrinsic Invariant and Main Theoremmentioning

confidence: 99%

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Katayama

Sutherland

Takesaki

1995

Electron. Res. Announc. Amer. Math. Soc.

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Abstract. We announce in this article that i) to each approximately finite dimensional factor R of any type there corresponds canonically a group cohomological invariant, to be called the intrinsic invariant of R and denoted Θ(R), on which Aut(R) acts canonically; ii) when a group G acts on R via α : G → Aut(R), the pull back of Orb(Θ(R)), the orbit of Θ(R) under Aut(R),by α is a cocycle conjugacy invariant of α; iii) if G is a discrete countable amenable group, then the pair of the module, mod(α), and the above pull back is a complete invariant for the cocycle conjugacy class of α. This result settles the open problem of the general cocycle conjugacy classification of discrete amenable group actions on an AFD factor of type III 1 , and unifies known results for other types.

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“…Our idea of a proof is using the continuous decomposition instead of the discrete decomposition based on the method in [14] and [15]. But in this case, we treat 2054 TOSHIHIKO MASUDA only factors of type III λ , 0 < λ < 1, with the trivial characteristic invariants, so the proof is less complicated than those in [14] and [15].…”

Section: Introductionmentioning

confidence: 99%

“…But in this case, we treat 2054 TOSHIHIKO MASUDA only factors of type III λ , 0 < λ < 1, with the trivial characteristic invariants, so the proof is less complicated than those in [14] and [15]. By using the continuous decomposition, we can more easily reduce the classification problem to the type II ∞ case than using the discrete decomposition and this method is valid for arbitrary discrete amenable groups.…”

Section: Introductionmentioning

confidence: 99%