Coarse structures and group actions

N. Brodskiy; J. Dydak; A. Mitra

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Triangular Actions on C3.

Dennis M. Snow (1988)

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$ℂ^{*}$ -actions on $ℂ^{3}$ are linearizable.

Kaliman, Shulim I., Koras, Mariusz, Makar-Limanov, Leonid, Russell, Peter (1997)

Electronic Research Announcements of the American Mathematical Society [electronic only]

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Hilbert C*-modules and amenable actions

Ronald G. Douglas, Piotr W. Nowak (2010)

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We study actions of discrete groups on Hilbert C*-modules induced from topological actions on compact Hausdorff spaces. We show non-amenability of actions of non-amenable and non-a-T-menable groups, provided there exists a quasi-invariant probability measure which is sufficiently close to being invariant.

The action of groups on real factors of type III $_{λ}$ , $λ \neq 1$ .

Rakhimov, A.A. (2004)

Zapiski Nauchnykh Seminarov POMI

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Amenable actions of nonamenable groups.

Grigorchuk, R.I., Nekrashevych, V.Yu. (2005)

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Rigidity results for Bernoulli actions and their von Neumann algebras

Stefaan Vaes (2005-2006)

Séminaire Bourbaki

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Using very original methods from operator algebras, Sorin Popa has shown that the orbit structure of the Bernoulli action of a property (T) group, completely remembers the group and the action. This information is even essentially contained in the crossed product von Neumann algebra. This is the first von Neumann strong rigidity theorem in the literature. The same methods allow Popa to obtain II $_{1}$ factors with prescribed countable fundamental group.