The KK-Theory of Fundamental C*-Algebras
| Autor: | Emmanuel Germain, Pierre Fima |
|---|---|
| Přispěvatelé: | Laboratoire de Mathématiques Nicolas Oresme (LMNO), Centre National de la Recherche Scientifique (CNRS)-Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Normandie Université (NU), 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) |
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Pure mathematics
Mathematics::Operator Algebras Applied Mathematics General Mathematics 010102 general mathematics [MATH.MATH-OA]Mathematics [math]/Operator Algebras [math.OA] Mathematics - Operator Algebras K-Theory and Homology (math.KT) KK-theory 01 natural sciences 0103 physical sciences Mathematics - K-Theory and Homology FOS: Mathematics 010307 mathematical physics 0101 mathematics Operator Algebras (math.OA) ComputingMilieux_MISCELLANEOUS Mathematics |
| Zdroj: | Transactions of the American Mathematical Society Transactions of the American Mathematical Society, American Mathematical Society, 2018, 370 (10), pp.7051-7079. ⟨10.1090/tran/7211⟩ |
| ISSN: | 0002-9947 |
| DOI: | 10.1090/tran/7211⟩ |
| Popis: | Given a graph of C*-algebras, we prove a long exact sequence in KK-theory for both the maximal and the vertex-reduced fundamental C*-algebras in the presence of possibly non GNS-faithful conditional expectations. We deduce from it the KK-equivalence between the full fundamental C*-algebra and the vertex-reduced fundamental C*-algebra even for non GNS-faithful conditional expectations. Our results unify, simplify and generalize all the previous results obtained before by Cuntz, Pimsner, Germain and Thomsen. It also generalizes the previous results of the authors on amalgamated free products. V1, 27p: the paper arXiv:1510.02418 has been splitted into two papers. It is the second part on fundamental C*-algebras |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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