The KK-theory of amalgamated free products

Emmanuel Germain (1) , Pierre Fima (2)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme
2 IMJ - Institut de Mathématiques de Jussieu

We prove a long exact sequence in KK-theory for both full and reduced amalgamated free products in the presence of conditional expectations. In the course of the proof, we established the KK-equivalence between the full amalgamated free product of two unital C*-algebras and a newly defined reduced amalgamated free product that is valid even for non GNS-faithful conditional expectations. Our results unify, simplify and generalize all the previous results obtained before by Cuntz, Germain and Thomsen.

Domains: Mathematics [math]; Operator Algebras [math.OA]; Mathematics [math]; K-Theory and Homology [math.KT]

Emmanuel Germain, Pierre Fima. The KK-theory of amalgamated free products. 2022. ⟨hal-01876567⟩