Injective factors

This course classifies the injective factors with separable predual that are not of type III₁: the hyperfinite factor is the only injective factor of type II₁, there is only one of type II∞ and one of each type IIIλ with 0 < λ < 1, and the injective factors of type III₀ are the Krieger factors, classified by their flow of weights. It also shows that injectivity, approximate finite dimensionality, semidiscreteness and property P coincide for factors with separable predual (for type III₁ with the help of a later uniqueness theorem, used without proof), building on trace inequalities, property Γ and approximately inner and centrally trivial automorphisms. Basic references are [Connes 1976], [Connes 1973], [Takesaki III], [Anantharaman–Popa] and [Connes 1994].

1. Trace inequalities for finite von Neumann algebras
2. Property Γ and the algebra generated by a factor and its commutant
3. Approximately inner and centrally trivial automorphisms
4. Injective von Neumann algebras
5. Uniqueness of the injective II₁ factor
6. Classification of injective factors

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