Some remarks in $C^*$- and $K$-theory

Bernhard Burgstaller

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arXiv · 1905.03504

Some remarks in $C^*$- and $K$-theory

Bernhard Burgstaller

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Abstract

This note consists of three unrelated remarks. First, we demonstrate how roughly speaking $*$-homomorphisms between matrix stable $C^*$-algebras are exactly the uniformly continuous $*$-preserving group homomorphisms between their genral linear groups. Second, using the Cuntz picture in $KK$-theory we bring morphisms in $KK$-theory represented by generators and relations to a particular simple form. Third, we show that for an inverse semigroup its associated groupoid is Hausdorff if and only if the inverse semigroup is $E$-continuous.

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Bernhard Burgstaller. 2019-05-09. Some remarks in $C^*$- and $K$-theory. https://arxiv.org/abs/1905.03504

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