Article
K-homology and K-theory for the lamplighter groups of finite groups
Author/s | Flores Díaz, Ramón Jesús
Pooya, Sanaz Valette, Alain |
Department | Universidad de Sevilla. Departamento de Geometría y Topología |
Publication Date | 2017-08 |
Deposit Date | 2017-09-05 |
Published in |
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Abstract | 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 ... 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. |
Funding agencies | Ministerio de Ciencia e Innovación (MICIN). España National Science Foundation (NSF). United States |
Project ID. | MTM2010-20692
DMS-1440140 |
Citation | Flores Díaz, R.J., Pooya, S. y Valette, A. (2017). K-homology and K-theory for the lamplighter groups of finite groups. Proceedings of the London Mathematical Society |
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