Compact operators and algebraic K -theory for groups which act properly and isometrically on Hilbert space
We prove the K-theoretic Farrell-Jones conjecture for groups with the Haagerup approximation property and coefficient rings and C ∗ C^{∗} -algebras which are stable with respect to compact operators. We use this and Higson-Kasparov's result that the Baum-Connes conjecture holds for such a group...
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todo:paper_00754102_v2018_n734_p265_Cortinas2023-10-03T14:53:55Z Compact operators and algebraic K -theory for groups which act properly and isometrically on Hilbert space Cortiñas, G. Tartaglia, G. We prove the K-theoretic Farrell-Jones conjecture for groups with the Haagerup approximation property and coefficient rings and C ∗ C^{∗} -algebras which are stable with respect to compact operators. We use this and Higson-Kasparov's result that the Baum-Connes conjecture holds for such a group G, to show that the algebraic and the C ∗ C^{∗} -crossed product of G with a stable separable G- C ∗ C^{∗} -algebra have the same K-theory. © 2018 Walter de Gruyter GmbH, Berlin/Boston. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00754102_v2018_n734_p265_Cortinas |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| description |
We prove the K-theoretic Farrell-Jones conjecture for groups with the Haagerup approximation property and coefficient rings and C ∗ C^{∗} -algebras which are stable with respect to compact operators. We use this and Higson-Kasparov's result that the Baum-Connes conjecture holds for such a group G, to show that the algebraic and the C ∗ C^{∗} -crossed product of G with a stable separable G- C ∗ C^{∗} -algebra have the same K-theory. © 2018 Walter de Gruyter GmbH, Berlin/Boston. |
| format |
JOUR |
| author |
Cortiñas, G. Tartaglia, G. |
| spellingShingle |
Cortiñas, G. Tartaglia, G. Compact operators and algebraic K -theory for groups which act properly and isometrically on Hilbert space |
| author_facet |
Cortiñas, G. Tartaglia, G. |
| author_sort |
Cortiñas, G. |
| title |
Compact operators and algebraic K -theory for groups which act properly and isometrically on Hilbert space |
| title_short |
Compact operators and algebraic K -theory for groups which act properly and isometrically on Hilbert space |
| title_full |
Compact operators and algebraic K -theory for groups which act properly and isometrically on Hilbert space |
| title_fullStr |
Compact operators and algebraic K -theory for groups which act properly and isometrically on Hilbert space |
| title_full_unstemmed |
Compact operators and algebraic K -theory for groups which act properly and isometrically on Hilbert space |
| title_sort |
compact operators and algebraic k -theory for groups which act properly and isometrically on hilbert space |
| url |
http://hdl.handle.net/20.500.12110/paper_00754102_v2018_n734_p265_Cortinas |
| work_keys_str_mv |
AT cortinasg compactoperatorsandalgebraicktheoryforgroupswhichactproperlyandisometricallyonhilbertspace AT tartagliag compactoperatorsandalgebraicktheoryforgroupswhichactproperlyandisometricallyonhilbertspace |
| _version_ |
1807314771142246400 |