Induction in stages for crossed products of C*-algebras by maximal coactions

2006/02/10 by Astrid an Huef, Huef, Astrid an, S. Kaliszewski +5
Mathematics · #46L55 #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics #math.OA #msc:46L55

paper · pdf · doi:10.48550/arxiv.math/0602222

38 pages, LaTeX, uses Xy-pic; significant reorganization of previous version; short section on regularity of induced representations added

openalex publication_date 2006/02/10 · arxiv created 2007/04/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let B be a C*-algebra with a maximal coaction of a locally compact group G, and let N and H be closed normal subgroups of G with N contained in H. We show that the process Ind_(G/H)^G which uses Mansfield's bimodule to induce representations of the crossed product of B by G from those of the restricted crossed product of B by (G/H) is equivalent to the two-stage induction process: Ind_(G/N)^G composed with Ind_(G/H)^(G/N). The proof involves a calculus of symmetric imprimitivity bimodules which relates the bimodule tensor product to the fibred product of the underlying spaces.

Citations

• Crossed Products by Dual Coactions of Groups and Homogeneous Spaces

Related

• Duality of Restriction and Induction for C^*-Coactions
• Crossed Products by Dual Coactions of Groups and Homogeneous Spaces
• Mansfield's imprimitivity theorem for full crossed products
• Three Bimodules for Mansfield's Imprimitivity Theorem
• Full and reduced coactions of locally compact groups on C*-algebras