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Published in:
2008 | OriginalPaper | Chapter
On Homotopical Non-invertibility of C*-extensions
Author : Vladimir Manuilov
Published in: Operator Algebras, Operator Theory and Applications
Publisher: Birkhäuser Basel
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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.