Three bimodules for Mansfield's imprimitivity theorem

Research output: Contribution to journalArticle

Abstract

For a maximal coaction δ of a discrete group G on a C*-algebra A and a normal subgroup N of G, there are at least three natural A xδ G x̂δl N - A xδl G/N imprimitivity bimodules: Mansfield's bimodule YGG/N (A); the bimodule assembled by Ng from Green's A xδ G x̂δ G x̂̂δl G/N - A xδ G x̂δ N imprimitivity bimodule XGN(A xδ G) and Katayama duality; and the bimodule assembled from XGN(A xδ G) and the crossed-product Mansfield bimodule YGG/G(A) x G/N. We show that all three of these are isomorphic, so that the corresponding inducing maps on representations are identical. This can be interpreted as saying that Mansfield and Green induction are inverses of one another 'modulo Katayama duality'. These results pass to twisted coactions; dual results starting with an action are also given.

Original languageEnglish (US)
Pages (from-to)397-419
Number of pages23
JournalJournal of the Australian Mathematical Society
Volume71
Issue number3
DOIs
StatePublished - Dec 2001

Keywords

  • C*-algebra
  • Coaction
  • Duality

ASJC Scopus subject areas

  • Mathematics(all)

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