Journal of Noncommutative Geometry

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Volume 2, Issue 3, 2008, pp. 263–282
DOI: 10.4171/JNCG/21

Published online: 2008-09-30

Properly infinite C(X)-algebras and K1-injectivity

Étienne Blanchard[1], Randi Rohde[2] and Mikael Rørdam[3]

(1) Institut de Mathématiques de Jussieu, Paris
(2) University of Southern Denmark, Odense
(3) University of Southern Denmark, Odense

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 of whether every unital properly infinite C*-algebra is K1-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.

Keywords: K1-injectivity, proper infiniteness

Blanchard Étienne, Rohde Randi, Rørdam Mikael: Properly infinite C(X)-algebras and K1-injectivity. J. Noncommut. Geom. 2 (2008), 263-282. doi: 10.4171/JNCG/21