New Titles  |  FAQ  |  Keep Informed  |  Review Cart  |  Contact Us Quick Search (Advanced Search ) Browse by Subject General Interest Logic & Foundations Number Theory Algebra & Algebraic Geometry Discrete Math & Combinatorics Analysis Differential Equations Geometry & Topology Probability & Statistics Applications Mathematical Physics Math Education
 Mémoires de la Société Mathématique de France 2008; 122 pp; softcover Number: 109 ISBN-10: 2-85629-233-X ISBN-13: 978-2-85629-233-4 List Price: US$40 Individual Members: US$36 Order Code: SMFMEM/109 In this volume, the author gives a definition for measured quantum groupoids. He aims to construct objects with duality including both quantum groups and groupoids. J. Kustermans and S. Vaes' works about locally compact quantum groups the author generalizes thanks to formalism introduced by M. Enock and J. M. Vallin in the case of inclusion of von Neumann algebras. From a structure of Hopf-bimodule with left and right invariant operator-valued weights, the author defines a fundamental pseudo-multiplicative unitary. To get a satisfying duality in the general case, he assumes the existence of an antipode given by its polar decomposition. This theory is illustrated with many examples, among them the inclusion of von Neumann algebras (M. Enock) and a sub family of measured quantum groupoids with easier axiomatic. A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list. Readership Graduate students and research mathematicians interested in analysis. Table of Contents Introduction Recalls Fundamental pseudo-multiplicative unitary Part I. Measured quantum groupoids Definition Uniqueness, modulus and scaling operator A density theorem Manageability of the fundamental unitary Duality Part II. Examples Adapted measured quantum groupoids Groupoids Finite quantum groupoids Quantum groups Compact case Quantum space quantum groupoid Pairs quantum groupoid Inclusions of von Neumann algebras Operations on adapted measured quantum groupoids Bibliography