Properly infinite C(X)-algebras and K_1-injectivity
Operator Algebras
2010-11-24 v1
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 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.
Keywords
Cite
@article{arxiv.0704.1554,
title = {Properly infinite C(X)-algebras and K_1-injectivity},
author = {Etienne Blanchard and Randi Rohde and Mikael Rordam},
journal= {arXiv preprint arXiv:0704.1554},
year = {2010}
}
Comments
19 pages