The KK-theory of amalgamated free products

Authors :: Emmanuel Germain
Pierre Fima
Institut de Mathématiques de Jussieu (IMJ)
Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)
Laboratoire de Mathématiques Nicolas Oresme (LMNO)
Centre National de la Recherche Scientifique (CNRS)-Université de Caen Normandie (UNICAEN)
Normandie Université (NU)-Normandie Université (NU)
Source :: Advances in Mathematics, Advances in Mathematics, Elsevier, 2020, 369, pp.107174. ⟨10.1016/j.aim.2020.107174⟩
Publication Year :: 2020
Publisher :: HAL CCSD, 2020.
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.<br />V.3, the paper has been splitted into two papers, this is the first part on amalgamated free products

Language :: English
ISSN :: 00018708 and 10902082
Database :: OpenAIRE
Journal :: Advances in Mathematics, Advances in Mathematics, Elsevier, 2020, 369, pp.107174. ⟨10.1016/j.aim.2020.107174⟩
Accession number :: edsair.doi.dedup.....3a11600d0e62c4f753aaf1ec974de35f

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