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

V. Manuilov·K. Thomsen
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Abstract

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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V. Manuilov, K. Thomsen. 2005-01-24. On the lack of inverses to C*-extensions related to property T groups. https://arxiv.org/abs/math/0501412

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