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The KK-theory of amalgamated free products

Emmanuel Germain
Pierre Fima
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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.
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hal-01876567 , version 1 (20-05-2022)


Attribution - NonCommercial - CC BY 4.0



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


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