Strong rigidity of generalized Bernoulli actions and computations of their symmetry groups

By Sorin Popa, S. Vaes. 2006

101 citations recorded by the source corpus.

Abstract We study equivalence relations and II 1 factors associated with (quotients of) generalized Bernoulli actions of Kazhdan groups. Specific families of these actions are entirely classified up to isomorphism of II 1 factors. This yields explicit computations of outer automorphism and fundamental groups. In particular, every finitely presented group is concretely realized as the outer automorphism group of a continuous family of non stably isomorphic II 1 factors.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/433ead0ab20ced7610060ad6ffefc4b021023aec

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In Algebra and Number Theory

In Mathematical Physics

Citations in the corpus

A CLASS OF SUPERRIGID GROUP VON NEUMANN ALGEBRAS (2010, methodology): “-amenable centralizer. Playing rigidity against deformability properties of an algebra in this manner became a paradigm of deformation/rigidity theory (see [Po01a, Po03, Po04, Po06a, Po06b]). Then in [PV06] it was realized that if Γ y Iis of the form Γ y Γ/Γ0, with Γ0 a “malnormal” subgroup of Γ, th”
W*‐superrigidity for group von Neumann algebras of left–right wreath products (2012, background): “groups such that two groups G and Λ in the class C must be isomorphic whenever they have isomorphic group II1 factors; see, for example, [12, 21, 23, 26].”
Q-system completion for C⁎ 2-categories (2021, unknown): “The first part (P1) is a generalization of the notoriously difficult problem of classifying group actions on II 1 factors up to cocycle conjugacy [Con75, Con77, Jon80, Ocn80] [IPP08, PV08, FV08], while the second part (P2) can be viewed as a non-abelian cohomology problem internal to C .”
A SURVEY OF MEASURED GROUP THEORY (2009, background): “I would like to express my deep appreciation to Bob Zimmer for his singular contribution to the subject.”
Group measure space decomposition of II1 factors and W*-superrigidity (2009, methodology): “In [ 51, Theorem 7.13 ], we provided a family of (generalized) wreath product groups satisfying such a strong rigidity result.”
Orbit Equivalence and Measured Group Theory (2010, background): “This property (never satisﬁed by standard Bernoulli shifts) entails several rigidity phenomena (see for instance [Pop06a, IPP08, GP05]).”
W*-superrigidity for Bernoulli actions of property (T) groups (2010, background): “Recently, more examples have been exhibited in [17] and [40].”
On Popa's Cocycle Superrigidity Theorem (2006, background): “As a result we do not discuss at all the results on von Neumann equivalence of group actions, and refer the reader to the above mentioned papers (see also [29]).”