On the lack of inverses to C*-extensions related to property T groups

Details On the lack of inverses to C*-extensions related to property T groups On the lack of inverses to C*-extensions related to property T groups

2005-01-24

arxiv.org/abs/math/0501412v1

Mathematics

Operator Algebras

11 pages

Scientific paper

Using ideas of S. Wassermann on non-exact $C^*$-algebras and property T
groups, we show that one of his examples of non-invertible C*-extensions is not
semi-invertible. To prove this, we show that a certain element vanishes in the
asymptotic tensor product. We also show that a modification of the example
gives a C*-extension which is not even invertible up to homotopy.

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