Hochschild Cohomology of Von Neumann Algebras [Paperback]

This book gives an introduction to biotransformations, the practice of harnessing biological catalysts for the preparation of useful chemicals.The subject of this book is the continuous Hochschild cohomology of dual normal modules over a von Neumann algebra. The material covered lies in the area common to Banach algebras, operator algebras and homological algebra, and will be of interest to researchers from these fields.The subject of this book is the continuous Hochschild cohomology of dual normal modules over a von Neumann algebra. The material covered lies in the area common to Banach algebras, operator algebras and homological algebra, and will be of interest to researchers from these fields.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.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. The authors...have succeeded in providing a very attractive account which will encourage researchers and graduate students... C.J.K. Batty, Mathematical Reviews Because of its clear and efficient presentation of material from many directions of research, Hochschild cohomology of vonlƒo