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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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Preprints, Working Papers, ...
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Contributor : Emmanuel Germain <>
Submitted on : Tuesday, September 18, 2018 - 3:21:36 PM
Last modification on : Wednesday, December 9, 2020 - 3:14:47 PM

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  • HAL Id : hal-01876567, version 1
  • ARXIV : 1510.02418



Emmanuel Germain, Pierre Fima. The KK-theory of amalgamated free products. 2018. ⟨hal-01876567⟩



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