On Homotopical Non-invertibility of C*-extensions
We have presented recently an example of a C*-extension, which is not invertible in the semigroup of homotopy classes of C*-extensions. Here we reveal the cause for existence of homotopy non-invertible C*-extensions: it is related to non-exact C*-algebras and to possibility to distinguish different tensor C*-norms by K-theory. We construct a special C*-algebra, K-theory of which hosts an obstruction for homotopical non-invertibility, and show that this obstruction for our example does not vanish.
KeywordsC*-algebra C*-extension homotopy
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