Properly infinite C(X)-algebras and K_1-injectivity
Résumé
We investigate if a unital $C(X)$-algebra is properly infinite when all its fibres are properly infinite. We show that this question can be rephrased in several different ways, including the question if every unital properly infinite \Cs{} is $K_1$-injective. We provide partial answers to these questions, and we show that the general question on proper infiniteness of $C(X)$-algebras can be reduced to establishing proper infiniteness of a specific $C([0,1])$-algebra with properly infinite fibres.
Domaines
Algèbres d'opérateurs [math.OA]
Origine : Fichiers produits par l'(les) auteur(s)
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