A 1-COHOMOLOGY CHARACTERIZATION OF PROPERTY (T) IN VON NEUMANN ALGEBRAS by JESSE PETERSON

A 1-cohomology Characterization of Property (t) in Von Neumann Algebras

We obtain a characterization of property (T) for von Neumann algebras in terms of 1-cohomology similar to the Delorme-Guichardet Theorem for groups.

L-rigidity in von Neumann algebras

We introduce the notion of L2-rigidity for von Neumann algebras, a generalization of property (T) which can be viewed as an analogue for the vanishing of 1-cohomology into the left regular representation of a group. We show that L2-rigidity passes to normalizers and is satisfied by nonamenable II1 factors which are non-prime, have property Γ , or are weakly rigid. As a consequence we obtain tha...

L 2 -rigidity in von Neumann algebras

We introduce the notion of L2-rigidity for von Neumann algebras, a generalization of property (T) which can be viewed as an analogue for the vanishing of 1-cohomology into the left regular representation of a group. We show that L2rigidity passes to normalizers and is satisfied by nonamenable II1 factors which are non-prime, have property Γ, or are weakly rigid. As a consequence we obtain that ...

ON THE NOTION OF RELATIVE PROPERTY (T) FOR INCLUSIONS OF VON NEUMANN ALGEBRAS by JESSE PETERSON and SORIN POPA*

We prove that the notion of rigidity (or relative property (T)) for inclusions of finite von Neumann algebras defined in [Po1] is equivalent to a weaker property, in which no “continuity constants” are required. The notion of relative property (T) (or rigidity) for inclusions of finite von Neumann algebras with countable decomposable center was introduced in ([P1]) by requiring that one of the ...

Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras