Some remarks in $C^*$- and $K$-theory
Operator Algebras
2019-05-10 v1 K-Theory and Homology
Abstract
This note consists of three unrelated remarks. First, we demonstrate how roughly speaking -homomorphisms between matrix stable -algebras are exactly the uniformly continuous -preserving group homomorphisms between their genral linear groups. Second, using the Cuntz picture in -theory we bring morphisms in -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 -continuous.
Cite
@article{arxiv.1905.03504,
title = {Some remarks in $C^*$- and $K$-theory},
author = {Bernhard Burgstaller},
journal= {arXiv preprint arXiv:1905.03504},
year = {2019}
}