The KK-theory of amalgamated free products

2015/10/08 by Fima, Pierre, Emmanuel Germain, Germain, Emmanuel
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Operator Algebra Research #FOS: Mathematics #K-Theory and Homology (math.KT) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1510.02418

openalex publication_date 2015/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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