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Journal Articles Advances in Mathematics Year : 2020

The KK-theory of amalgamated free products

Pierre Fima
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Emmanuel Germain


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)


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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⟩
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