Hochschild Cohomology of Von Neumann Algebras

ISBN-13: 9780521478809 / Angielski / Miękka / 1995 / 208 str.

A. Sinclair; Roger R. Smith; Allan M. Sinclair

Opis

The subject of this book is the continuous Hochschild cohomology of dual normal modules over a von Neumann algebra. The authors develop the necessary technical results, assuming a familiarity with basic C*-algebra and von Neumann algebra theory, including the decomposition into types, but no prior knowledge of cohomology theory is required and the theory of completely bounded and multilinear operators is given fully. Those cases when the continuous Hochschild cohomology Hn(M, M) of the von Neumann algebra M over itself is zero are central to this book. The material in this book lies in the area common to Banach algebras, operator algebras and homological algebra, and will be of interest to researchers from these fields

Recenzje

'… a comprehensive and readable introduction to the field.' Monatshefte für Mathematik

Spis treści

Preface; 1. Introduction; 2. Completely bounded operators; 3. Derivations; 4. Averaging in continuous and normal cohomology; 5. Completely bounded cohomology; 6. Hyperfinite subalgebras; 7. Continuous cohomology; 8. Stability of products; 9Appendix; Bibliography; Notation; Index.