Categorical landstad duality for actions

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Abstract

We show that the category JA(G) of actions of a locally compact group G on C*-algebras (with equivariant nondegenerate*-homomorphisms into multiplier algebras) is equivalent, via a full-crossed-product functor, to a comma category of maximal coactions of G under the comultiplication (C*(G),5c); and also that JA(G) is equivalent, via a reduced- crossed-product functor, to a comma category of normal coactions under the comultiplication. This extends classical Landstad duality to a category equivalence, and allows us to identify those C*-algebras which are isomorphic to crossed products by G as precisely those which form part of an object in the appropriate comma category.

Original languageEnglish (US)
Pages (from-to)415-441
Number of pages27
JournalIndiana University Mathematics Journal
Volume58
Issue number1
DOIs
StatePublished - 2009

Keywords

  • Category equivalence
  • Comma category
  • Full crossed product
  • Landstad duality
  • Maximal coaction

ASJC Scopus subject areas

  • Mathematics(all)

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