2005/04/06 by Franck Lesieur, Lesieur, Franck · 1 citation
Mathematics · #46LXX #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:46LXX
paper · pdf · doi:10.48550/arxiv.math/0504104
139 pages. Retenu pour publication aux M{é}moires de la SMF
openalex publication_date 2005/04/06 · arxiv created 2007/03/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we give a definition for measured quantum groupoids. We want to get objects with duality extending both quantum groups and groupoids. We base ourselves on J. Kustermans and S. Vaes' works about locally compact quantum groups that we generalize 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, we define a fundamental pseudo-multiplicative unitary. To get a satisfying duality in the general case, we assume the existence of an antipode given by its polar decomposition. This theory is illustrated with many examples among others inclusion of von Neumann algebras (M. Enock) and a sub family of measured quantum groupoids with easier axiomatic.