Hochschild Cohomology of Von Neumann Algebras (London Mathematical Society Lecture Note Series, Series Number 203)

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. The continuous Hochschild cohomology of dual normal modules over a von Neumann algebra is the subject of this book. The necessary technical results are developed assuming a familiarity with basic C*-algebra and von Neumann algebra theory, including the decomposition into two types, but no prior knowledge of cohomology theory is required and the theory of completely bounded and multilinear operators is given fully. Central to this book are those cases when the continuous Hochschild cohomology H(superscript n)(M, M) of the von Neumann algebra M over itself is zero. 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. This is an introductory text intended to give the non-specialist a comprehensive insight into the science of biotransformations. The book traces the history of biotransformations, clearly spells out the pros and cons of conducting enzyme-mediated versus whole-cell bioconversions, and gives a variety of examples wherein the bio-reaction is a key element in a reaction sequence leading from cheap starting materials to valuable end products. This book is intended to give a non-specialist a comprehensive introduction to the science of biotransformations, the practice of harnessing biological catalysts for the preparation of useful fine chemicals such as pharmaceuticals, fragrances and flavours.