A NOTE ON MAXIMAL SUBFACTORS

In this note, we consider the maximal subfactors of factors. We show that there is no maximal subfactor of type In factors when n is finite. We also consider the relation between maximal subfactor and Jones' basic construction. In the end, we give an example of an index 2 maximal subfactor in free group factor with 2 generators.

Structural results for free Araki–Woods factors and their continuous cores

We show that for any type III1free Araki–Woods factor$\mathcal{M}$=(HR, Ut)″ associated with an orthogonal representation(Ut)ofRon a separable real Hilbert spaceHR, the continuous coreM=$\mathcal{M}$⋊σRis a semisolid II∞factor, i.e. for any non-zero finite projectionq∈M, the II1factorqM qis semisolid. If the representation(Ut)is moreover assumed to be mixing, then we prove that the coreMis solid. As an application, we construct an example of a non-amenable solid II1factorNwith full fundamental group, i.e.$\mathcal{F}$(N) =R*+, which is not isomorphic to any interpolated free group factorL(Ft), for 1 <t≤ = +∞.

ON A SUBFACTOR CONSTRUCTION OF A FACTOR NON-ANTIISOMORPHIC TO ITSELF

We define a ℤ3-kernel α on [Formula: see text] and a ℤ3-kernel β on the hyperfinite II 1 factor R, which have conjugate obstruction to lifting. Hence, α⊗β can be perturbed by an inner automorphism to produce an action γ on [Formula: see text]. The aim of this paper is to show that the factor [Formula: see text], which is similar to Connes's example of a II 1 factor non-antiisomorphic to itself, is the enveloping algebra of an inclusion of II 1 factors A⊂B. Here A is an interpolated free group factor and B is isomorphic to the crossed product A⋊θℤ9, where θ is a ℤ3-kernel of A with non-trivial obstruction to lifting. By using an argument due to Connes, which involves the invariant χ(ℳ), we show that ℳ is not anti-isomorphic to itself. Furthermore, we prove that for one of the generator of χ(ℳ), which we will denote by σ, the Jones invariant ϰ(σ) is equal to [Formula: see text].