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On the structural theory of  II 1 factors of negatively curved groups

Ionut Chifan, Thomas Sinclair (2013)

Annales scientifiques de l'École Normale Supérieure

Ozawa showed in [21] that for any i.c.c. hyperbolic group, the associated group factor L Γ is solid. Developing a new approach that combines some methods of Peterson [29], Ozawa and Popa [27, 28], and Ozawa [25], we strengthen this result by showing that L Γ is strongly solid. Using our methods in cooperation with a cocycle superrigidity result of Ioana [12], we show that profinite actions of lattices in  Sp ( n , 1 ) , n 2 , are virtually W * -superrigid.

On Woronowicz's approach to the Tomita-Takesaki theory

László Zsidó (2012)

Banach Center Publications

The Tomita-Takesaki Theory is very complex and can be contemplated from different points of view. In the decade 1970-1980 several approaches to it appeared, each one seeking to attain more transparency. One of them was the paper of S. L. Woronowicz "Operator systems and their application to the Tomita-Takesaki theory" that appeared in 1979. Woronowicz's approach allows a particularly precise insight into the nature of the Tomita-Takesaki Theory and in this paper we present a brief, but fairly detailed...

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