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The KK-theory of amalgamated free products

Abstract : 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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https://hal-normandie-univ.archives-ouvertes.fr/hal-01876567
Contributor : emmanuel germain Connect in order to contact the contributor
Submitted on : Friday, May 20, 2022 - 11:01:11 AM
Last modification on : Saturday, May 21, 2022 - 3:51:20 AM

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

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