K-homology and K-theory for the lamplighter groups of finite groups
Let F be a finite group. We consider the lamplighter group L = F ≀ Z over F. We prove that L has a classifying space for proper actions EL which is a complex of dimension 2.We use this to give an explicit proof of the Baum–Connes conjecture (without coefficients) that states that theassembly map µLi: K...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2017 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/64166 |
| Acceso en línea: | http://hdl.handle.net/11441/64166 https://doi.org/10.1112/plms.12061 |
| Access Level: | acceso abierto |
| Palabra clave: | K-theory C ∗ -algebra Proper actions Baum-Connes conjecture |
| Sumario: | Let F be a finite group. We consider the lamplighter group L = F ≀ Z over F. We prove that L has a classifying space for proper actions EL which is a complex of dimension 2.We use this to give an explicit proof of the Baum–Connes conjecture (without coefficients) that states that theassembly map µLi: KLi(E L) → Ki(C∗L)(i =0, 1) is an isomorphism. Actually, K0(C∗L) is free abelian of countable rank, with an explicit basis consisting of projections in C∗L, while K1(C∗L) is infinite cyclic, generated by the unitary of C∗L implementing t he shift. Finally we show that,for F abelian, the C∗-algebra C∗L is completely characterized by |F | up to isomorphism. |
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