A Survey of Hochschild Cohomology for von Neumann Algebras

On Cyclic Vectors and Thin Von Neumann Algebras

We prove that certain classes of von Neumann algebras with regular, injective subalgebras are thin. As a consequence, all Hochschild cohomology groups of these algebras are zero. Mathematics subject classification (2010): 46L10, 47A16.

Second Hochschild Cohomology of Convolution Algebras

The hochschild cohomology problem for von neumann algebras.

In 1967, when Kadison and Ringrose began the development of continuous cohomology theory for operator algebras, they conjectured that the cohomology groups Hn(M, M), n >/= 1, for a von Neumann algebra M, should all be zero. This conjecture, which has important structural implications for von Neumann algebras, has been solved affirmatively in the type I, IIinfinity, and III cases, leaving open o...

A Cohomological Characterization of Approximately Finite Dimensional Von Neumann Algebras

One of the purposes in the computation of cohomology groups is to establish invariants which may be helpful in the classification of the objects under consideration. In the theory of continuous Hochschild cohomology for operator algebras R. V. Kadison and J. R. Ringrose proved [10] that for any hyperfinite von Neumann algebra M and any dual normal M-bimodule S, all the continuous cohomology gro...

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 ...