The KK-theory of amalgamated free products
Pierre Fima, Emmanuel Germain
TL;DR
This paper establishes a long exact sequence in KK-theory for amalgamated free products of C*-algebras, unifying and generalizing previous results and introducing a new reduced product applicable even for non GNS-faithful expectations.
Contribution
It proves a KK-theory exact sequence for amalgamated free products and introduces a new reduced product that broadens applicability beyond GNS-faithful cases.
Findings
Established KK-equivalence between full and reduced amalgamated free products.
Unified and extended previous KK-theory results by Cuntz, Germain, and Thomsen.
Provided a framework valid for non GNS-faithful conditional expectations.
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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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Algebra and Logic