Von Neumann Equivalence in Deformation Rigidity Theory
Kasiwatte Kankanamge, Dumindu Sandakith
0009-0003-6349-305X
:
2023-06-01
Abstract
Ishan, Peterson and Ruth introduced the notion of von Neumann equivalence as
a non-commutative analogue of measure equivalence. They showed approximation
properties like amenability, property (T) and Haagerup property are invariant under
von Neumann equivalence in the group case. We show that
these results can be extended to the von Neumann algebras by inducing bimodules
through von Neumann equivalence. We also prove that proper proximality and $L^2$-rigidity are preserved under von Neumann equivalence.