Local and global proper infiniteness for continuous C(X)-algebras

Etienne Blanchard (1)

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche

We show that all unital continuous C*-bundles with properly infinite fibres are properly infinite C*-algebras if and only if the full unital free product of two copies of the Cuntz extensions $\Td$ of the Cuntz algebra $\mathcal{O}_2$ by the \cst-algebra of compact operators is a $K_1$-injective \cst-algebra.

Mots clés: Classification of continuous fields of C*-algebras; K_1-injectivity

Domaines: Algèbres d'opérateurs [math.OA]

Etienne Blanchard. Local and global proper infiniteness for continuous C(X)-algebras. 2013. ⟨hal-00922786v3⟩