L-cohomology for Von Neumann Algebras

Various topological forms of Von Neumann regularity in Banach algebras

We study topological von Neumann regularity and principal von Neumann regularity of Banach algebras. Our main objective is comparing these two types of Banach algebras and some other known Banach algebras with one another. In particular, we show that the class of topologically von Neumann regular Banach algebras contains all $C^*$-algebras, group algebras of compact abelian groups and ...

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

L-homology for Von Neumann Algebras

The aim of this paper is to introduce a notion of L-homology in the context of von Neumann algebras. Finding a suitable (co)homology theory for von Neumann algebras has been a dream for several generations (see [KR71a, KR71b, JKR72, SS95] and references therein). One’s hope is to have a powerful invariant to distinguish von Neumann algebras. Unfortunately, little positive is known about the Kad...

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

We obtain a characterization of property (T) for von Neumann algebras in terms of 1-cohomology similar to the Delorme-Guichardet Theorem for groups. Throughout this paper N will denote a finite von Neumann algebra with a fixed normal faithful tracial state τ .

Vanishing of Second Cohomology for Tensor Products of Type Ii1 Von Neumann Algebras

We show that the second cohomology group H2(M⊗N, M⊗N) is always zero for arbitrary type II1 von Neumann algebras M and N .

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.