SMF

Ergodic actions of compact matrix pseudogroups on $C^{*}$-algebras

Ergodic actions of compact matrix pseudogroups on $C^{*}$-algebras

F.P. BOCA
     
                
  • Année : 1995
  • Tome : 232
  • Format : Électronique
  • Langue de l'ouvrage :
    Anglais
  • Class. Math. : 46L55
  • Pages : 93-109
  • DOI : 10.24033/ast.312

A generalization of the ical finiteness theorem of Høegh-Krohn, Landstad and Størmer for ergodic actions of compact groups on operator algebras is proved for actions of compact matrix pseudogroups on $C^*$-algebras. This, together with the Takesaki-Takai type duality result of Baaj and Skandalis, show that the reduced $C^*$-crossed product of a unital $C^*$ - algebra by an ergodic action of a compact matrix pseudogroup is a direct sum of $C^*$-algebras of compact operators



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