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arXiv · 1510.02418

The KK-theory of amalgamated free products

Pierre Fima·Emmanuel Germain
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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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Pierre Fima, Emmanuel Germain. 2015-10-08. The KK-theory of amalgamated free products. https://arxiv.org/abs/1510.02418

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