Strong solidity of group factors from lattices in SO(n,1) and SU(n,1)

Abstract

We show that the group factors of ICC lattices in either SO(n,1) or SU(n,1), n \geq 2, are strongly solid in the sense of Ozawa and Popa. This strengthens a result of Ozawa and Popa showing that these factors do not have Cartan subalgebras.

References in corpus (5)

• Group measure space decomposition of II_1 factors and W*-superrigidity
• On a class of ${\mathrm{II}}_1$ factors with at most one Cartan subalgebra
• Examples of group actions which are virtually W*-superrigid
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Cited by in corpus (18)

• On the structural theory of II_1 factors of negatively curved groups, II: Actions by product groups
• W*-superrigidity for group von Neumann algebras of left-right wreath products
• Some unique group-measure space decomposition results
• Strong solidity of free Araki-Woods factors
• Strong Solidity of the q-Gaussian Algebras for all -1 < q < 1
• Unique Cartan decomposition for II_1 factors arising from arbitrary actions of hyperbolic groups
• Primeness results for von Neumann algebras associated with surface braid groups
• Inner amenability for groups and central sequences in factors
• One-cohomology and the uniqueness of the group measure space decomposition of a II_1 factor
• Tensor product decompositions of II${}_1$ factors arising from extensions of amalgamated free product groups
• Maximal rigid subalgebras of deformations and $L^2$-cohomology
• Consequences of the random matrix solution to the Peterson-Thom conjecture
• Product rigidity in von Neumann and C${}^{\ast }$-algebras via s-malleable deformations
• Cohomological obstructions to lifting properties for full group C${}^{\ast }$-algebras
• Classification of Tensor Decompositions of II${}_1$ Factors Associated With Poly-Hyperbolic Groups
• Uniqueness of group-measure space Cartan subalgebras
• W${}^{\ast }$-superrigidity for wreath products with groups having positive first ${\ell }^2$-Betti number
• Classification of tensor decompositions for II${}_1$ factors