2007/12/21 by Thomas Timmermann, Timmermann, Thomas
Mathematics · #46L55 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:46L55
paper · pdf · doi:10.48550/arxiv.0712.3695
29 pages
arxiv created 2007/12/21 · openalex publication_date 2007/12/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the setting of von Neumann algebras, measurable quantum groupoids have successfully been axiomatized and studied by Enock, Vallin, and Lesieur, whereas in the setting of C*-algebras, a similar theory of locally compact quantum groupoids could not yet be developed. Some basic building blocks for such a theory, like analogues of a Hopf-von Neumann bimodule and of a pseudo-multiplicative unitary, were introduced in the thesis and a recent article by the author. That approach, however, is restricted to decomposable quantum groupoids which generalize r-discrete groupoids. Recently, we developed a general approach that covers all locally compact groupoids. In this article, we explain how the special theory of our thesis embeds into the general one.