K-theoretic amenability for SL2(Qp), and the action on the associated tree |
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| Authors: | Pierre Julg Alain Valette |
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| Affiliation: | Laboratoire de Mathématiques Fondamentales, Université Pierre et Marie Curie, Tour 45–46, 4, Place Jussieu, F-75230 Paris Cedex 05, France;Département de Mathématiques CP 214, Université Libre de Bruxelles, Boulevard du Triomphe, B-1050 Bruxelles, Belgium |
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| Abstract: | It is proved that if a locally compact group G acts simplicially on a tree in such a way that the stabilizers of the vertices are amenable, then G is K-amenable. In particular, the canonical map from the full C1-algebra onto the reduced C1-algebra of G induces isomorphisms in K-theory. The main corollary of our result is that SL2(Qp) and some other groups over local fields are K-amenable. |
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