Remarks on the diagonal embedding and strong 1-boundedness

2022/10/07 by Elayavalli, Srivatsav Kunnawalkam · 1 citation
#FOS: Mathematics #Group Theory (math.GR) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2210.03783

Abstract

We identify a large class of hyperbolic groups whose von Neumann algebras are not strongly 1-bounded: Sela's hyperbolic towers over F₂ subgroups. We also show that any intermediate subalgebra of the diagonal embedding of L(F₂) into its ultrapower doesn't have Property (T).

Cited by

• 50 Open Problems: Ultraproduct II₁ factors

Related

• Strong Property (T) and relatively hyperbolic groups
• Towers and elementary embeddings in toral relatively hyperbolic groups
• Maximal amenable subalgebras of von Neumann algebras associated with hyperbolic groups
• Solid von Neumann Algebras
• Strong accessibility for hyperbolic groups