2021/07/04 by Bernhard Burgstaller, Burgstaller, Bernhard
Mathematics · #16B50 #19K35 #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Operator Algebras (math.OA) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2107.01597
openalex publication_date 2021/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A group equivariant KK-theory for rings will be defined and studied in analogy to Kasparov's KK-theory for C^*-algebras. It is a kind of linearization of the category of rings by allowing addition of homomorphisms, imposing also homotopy invariance, invertibility of matrix corner embeddings, and allowing morphisms which are the opposite split of split exact sequences. We demonstrate the potential of this theory by proving for example equivalence induced by Morita equivalence and a Green-Julg isomorphism in this framework.