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