The hochschild cohomology problem for von neumann algebras.
Where this comes from
- Record sourced from PubMed, PMID 9520373.
- Also identified by PMC identifier 19843.
- No licence information is recorded for this record.
- Because redistribution is not established, this page shows the abstract only. Follow the links below for the full text.
Abstract
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 only the type II1 case. In this paper, we describe a positive solution when M is type II1 and has a Cartan subalgebra and a separable predual.