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Weakly proper group actions, Mansfield's imprimitivity and twisted Landstad duality

2013/10/15 by Alcides Buss, Buss, Alcides, Siegfried Echterhoff +1
Mathematics · #22D35 #46L55 #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Operator Algebras (math.OA) #math.OA #msc:22D35 #msc:46L55

paper · pdf · doi:10.48550/arxiv.1310.3934

29 pages. Revised version, to appear in Trans. Amer. Math. Soc

openalex publication_date 2013/10/15 · arxiv created 2014/05/30 · arxiv updated 2014/06/02 · openalex created_date 2025/10/27 · openalex updated_date 2026/07/28

Abstract

Using the theory of weakly proper actions of locally compact groups recently developed by the authors, we give a unified proof of both reduced and maximal versions of Mansfield's Imprimitivity Theorem and obtain a general version of Landstad's Duality Theorem for twisted group coactions. As one application, we obtain the stabilization trick for arbitrary twisted coactions, showing that every twisted coaction is Morita equivalent to an inflated coaction.

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