Memoirs of the American Mathematical Society 1993; 93 pp; softcover Volume: 106 ISBN10: 0821825755 ISBN13: 9780821825754 List Price: US$36 Individual Members: US$21.60 Institutional Members: US$28.80 Order Code: MEMO/106/506
 This work describes a general construction of a deformation quantization for any Poisson bracket on a manifold which comes from an action of \(R^d\) on that manifold. These deformation quantizations are strict, in the sense that the deformed product of any two functions is again a function and that there are corresponding involutions and operator norms. Many of the techniques involved are adapted from the theory of pseudodifferential operators. The construction is shown to have many favorable properties. A number of specific examples are described, ranging from basic ones such as quantum disks, quantum tori, and quantum spheres, to aspects of quantum groups. Readership Researchers and advanced graduate students, especially those working in quantum geometry. Table of Contents  Oscillatory integrals
 The deformed product
 Function algebras
 The algebra of bounded operators
 Functoriality for the operator norm
 Norms of deformed deformations
 Smooth vectors, and exactness
 Continuous fields
 Strict deformation quantization
 Old examples
 The quantum Euclidean closed disk and quantum quadrant
 The algebraists quantum plane, and quantum groups
 References
