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Browsing by Author Fernos, Talia

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  • Authors: Fernos, Talia (2006)

  • Relative property (T) has recently been used to show the existence of a variety of new rigidity phenomena, for example in von Neumann algebras and the study of orbit-equivalence relations. However, until recently there were few examples of group pairs with relative property (T) available through the literature. This motivated the following main result: A finitely gen¬erated group F admits a special linear representation with non-amenable 1l -Zariski closure if and only if it acts on an Abelian group A (of finite nonzero Q-rank) so that the corresponding group pair (F x A, A) has relative property (T). The proof is constructive. The main ingredients are Furstenberg's celebrated lemma ...