2016/02/09 by Bernhard Burgstaller, Burgstaller, Bernhard · 1 citation
Mathematics · #19K35 #46L80 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)
paper · pdf · doi:10.48550/arxiv.1602.03034
openalex publication_date 2016/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.