JournalsjncgVol. 2 , No. 3DOI 10.4171/jncg/21

Properly infinite <var>C</var>(<var>X</var>)-algebras and <var>K</var><sub>1</sub>-injectivity

  • Étienne Blanchard

    Institut de Mathématiques de Jussieu, Paris
  • Randi Rohde

    University of Southern Denmark, Odense
  • Mikael Rørdam

    University of Southern Denmark, Odense
Properly infinite <var>C</var>(<var>X</var>)-algebras and <var>K</var><sub>1</sub>-injectivity cover

Abstract

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.