ON THE STRUCTURAL THEORY OF II1 FACTORS OF NEGATIVELY CURVED GROUPS, II. ACTIONS BY PRODUCT GROUPS

By I. Chifan, Thomas Sinclair, Bogdan Udrea. 2011

71 citations recorded by the source corpus.

Abstract This paper contains a series of structural results for von Neumann algebras arising from measure preserving actions by product groups on probability spaces. Expanding upon the methods used earlier by the first two authors, we obtain new examples of strongly solid factors as well as von Neumann algebras with unique or no Cartan subalgebra. For instance, we show that every II 1 factor associated with a weakly amenable group in the class S of Ozawa is strongly solid. There is also the following product version of this result: any maximal abelian ⋆ -subalgebra of any II 1 factor associated with a finite product of weakly amenable groups in the class S of Ozawa has an amenable normalizing algebra. Finally, pairing some of these results with a cocycle superrigidity result of Ioana, it follows that compact actions by finite products of lattices in S p ( n , 1 ) , n ≥ 2 , are virtually W ∗ -superrigid.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/bed1ae5d9b1a73d1bf58d313c945e62d9f586652

Citations in the corpus

• Acylindrical hyperbolicity of groups acting on trees (2013, unknown): “ents in the left regular representation obtained in [17, 43, 50] also seem likely to be useful in the study of the structure of group von Neumann algebras via a further generalization of methods from [24, 25]. • Sisto [89] studied random walks on acylindrically hyperbolic groups using the language o”
• Unique prime factorization and bicentralizer problem for a class of type III factors (2015, unknown): “For other UPF results in the framework of II 1 factors, we refer the reader to [CKP14, CSU11, Pe06, Sa09, SW11].”