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arXiv · 1602.03034

The generators and relations picture of $KK$-theory

Bernhard Burgstaller
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Abstract

This is half an overview article since what we describe here is essentially known. We describe $KK$-theory by generators and relations in a formal sum of formal products of $*$-homomorphisms and some synthetical morphisms. What comes out is a category. The Kasparov product is then just the composition of morphisms. This description may be interesting to anyone who wants a quick and elementary definition of $KK$-theory. The description could also be used for other categories of algebras than $C^*$-algebras endowed with group actions, for example, $C^*$-algebras equipped with an action by a semigroup, a category et cetera.

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Bernhard Burgstaller. 2016-02-09. The generators and relations picture of $KK$-theory. https://arxiv.org/abs/1602.03034

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