The KK-theory of amalgamated free products

Pierre Fima (1) , Emmanuel Germain (2)

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

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.

Domaines: Algèbres d'opérateurs [math.OA]; K-théorie et homologie [math.KT]

Pierre Fima, Emmanuel Germain. The KK-theory of amalgamated free products. Advances in Mathematics, 2020, pp.107174. ⟨10.1016/j.aim.2020.107174⟩. ⟨hal-01876567⟩