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Measured Quantum Groupoids
Franck Lesieur, Université de Caen, France
A publication of the Société Mathématique de France.
cover
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
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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
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