Inclusions of von Neumann Algebras and Quantum groupoids III

2004/05/25 by Michel Enock, Enock, Michel · 1 citation
Mathematics · #46L37 #46L89 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA) #math.OA #math.QA #msc:46L37 #msc:46L89

paper · pdf · doi:10.48550/arxiv.math/0405480

arxiv created 2004/05/25 · openalex publication_date 2004/05/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In a former article, in collaboration with Jean-Michel Vallin, we have constructed two "quantum groupo"ıds" dual to each other, from a depth 2 inclusion of von Neumann algebras M₀⊂ M₁, in such a way that the canonical Jones'tower associated to the inclusion can be described as a tower of successive crossed-products by these two structures. We are now investigating in greater details these structures in the presence of an appropriate modular theory on the basis M'₀∩ M₁, and we show how these examples fit with Lesieur's "measured quantum groupo"ıds".

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• Depth 2 inclusions of simple C^*-algebras and their weak C^*-Hopf algebra symmetries

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