A CLASS OF SUPERRIGID GROUP VON NEUMANN ALGEBRAS

By Adrian Ioana, Sorin Popa, S. Vaes. 2010

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We prove that for any group G in a fairly large class of generalized wreath product groups, the associated von Neumann algebra LG completely \remembers" the group G. More precisely, if LG is isomorphic to the von Neumann algebra L of an arbitrary countable group , then must be isomorphic to G. This represents the rst superrigidity result pertaining to group von Neumann algebras.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e158605f51e1ff17993ac3aeb2bece0887f4e6f8

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In Algebra and Number Theory

In Mathematical Physics

Citations in the corpus

ON THE STRUCTURAL THEORY OF II1 FACTORS OF NEGATIVELY CURVED GROUPS, II. ACTIONS BY PRODUCT GROUPS (2011, background): “To list some of the major accomplishments which have occurred in the last several years: the cocycle superrigidity theorems of Popa [53, 55] and Ioana [25]; work on the classification of Cartan subalgebras by Ozawa and Popa [45, 46]; the discovery W∗-superrigid groups and actions with substantial co”
W*‐superrigidity for group von Neumann algebras of left–right wreath products (2012, methodology): “oup (Z/2Z)(Γ) ⋊(Γ × Γ) is W∗-superrigid. As we explain in Remark 6.2, this is however not true for arbitrary nonamenable icc groups Γ. To prove our W∗-superrigidity theorem, we follow the approach of [IPV10], by considering the comultiplication ∆ : LΛ → LΛ ⊗ LΛ that is induced by another group von N”
RIGIDITY FOR VON NEUMANN ALGEBRAS (2017, methodology): “ApplyingOE-superrigidity results from Popa [2007a, 2008] and Kida [2011] enabled them to provide the first concrete classes of W -superrigid actions.”