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Strongly Solid II1 Factors with an Exotic MASA
Using an extension of techniques of Ozawa and Popa, we give an example of a non-amenable strongly solid II 1 factor M containing an “exotic” maximal abelian subalgebra A: as an A,A-bimodule, L 2 (M)
On Some Free Products of Von Neumann Algebras which are Free Araki–Woods Factors
We prove that certain free products of factors of type I and other von Neumann algebras with respect to nontracial, almost periodic states are almost periodic free Araki–Woods factors. In particular,
Bass-Serre rigidity results in von Neumann algebras
We obtain new Bass-Serre type rigidity results for ${\rm II_1}$ equivalence relations and their von Neumann algebras, coming from free ergodic actions of free products of groups on the standard
Gamma Stability in Free Product von Neumann Algebras
Let $${(M, \varphi) = (M_1, \varphi_1) * (M_2, \varphi_2)}$$(M,φ)=(M1,φ1)∗(M2,φ2) be a free product of arbitrary von Neumann algebras endowed with faithful normal states. Assume that the centralizer
Strongly solid group factors which are not interpolated free group factors
We give examples of non-amenable infinite conjugacy classes groups Γ with the Haagerup property, weakly amenable with constant Λcb(Γ) = 1, for which we show that the associated II1 factors L(Γ) are
Stationary characters on lattices of semisimple Lie groups
We show that stationary characters on irreducible lattices Γ < G $\Gamma < G$ of higher-rank connected semisimple Lie groups are conjugation invariant, that is, they are genuine characters. This
A class of groups for which every action is W$^*$-superrigid
We prove the uniqueness of the group measure space Cartan subalgebra in crossed products A \rtimes \Gamma covering certain cases where \Gamma is an amalgamated free product over a non-amenable
Amalgamated free product type III factors with at most one Cartan subalgebra
Abstract We investigate Cartan subalgebras in nontracial amalgamated free product von Neumann algebras ${\mathop{M{}_{1} \ast }\nolimits}_{B} {M}_{2} $ over an amenable von Neumann subalgebra $B$.