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- Title
Structure of Relatively Biexact Group von Neumann Algebras.
- Authors
Ding, Changying; Elayavalli, Srivatsav Kunnawalkam
- Abstract
Using computations in the bidual of B (L 2 M) we develop a new technique at the von Neumann algebra level to upgrade relative proper proximality to full proper proximality. This is used to structurally classify subalgebras of L Γ where Γ is an infinite group that is biexact relative to a finite family of subgroups { Λ i } i ∈ I such that each Λ i is almost malnormal in Γ . This generalizes the result of Ding et al. (Properly proximal von Neumann algebras, 2022. ) which classifies subalgebras of von Neumann algebras of biexact groups. By developing a combination with techniques from Popa’s deformation-rigidity theory we obtain a new structural absorption theorem for free products and a generalized Kurosh type theorem in the setting of properly proximal von Neumann algebras.
- Publication
Communications in Mathematical Physics, 2024, Vol 405, Issue 4, p1
- ISSN
0010-3616
- Publication type
Article
- DOI
10.1007/s00220-024-04987-8