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Contracting automorphisms and$L$^{$p$}-cohomology in degree one

Yves Cornulier Institut de recherche mathématique de Rennes, Université de Rennes 1 Romain Tessera Département de mathématiques (UMPA) École normale supérieure de Lyon, 46 allée d’Italie, Lyon Cedex 07, France

Group Theory and Lie Theory mathscidoc:1701.17003

Arkiv for Matematik, 49, (2), 295-324, 2009.9
We characterize those Lie groups, and algebraic groups over a local field of characteristic zero, whose first reduced$L$^{$p$}-cohomology is zero for all$p$>1, extending a result of Pansu. As an application, we obtain a description of Gromov-hyperbolic groups among those groups. In particular we prove that any non-elementary Gromov-hyperbolic algebraic group over a non-Archimedean local field of zero characteristic is quasi-isometric to a 3-regular tree. We also extend the study to general semidirect products of a locally compact group by a cyclic group acting by contracting automorphisms.
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@inproceedings{yves2009contracting,
  title={Contracting automorphisms and$L$^{$p$}-cohomology in degree one},
  author={Yves Cornulier, and Romain Tessera},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203630465775003},
  booktitle={Arkiv for Matematik},
  volume={49},
  number={2},
  pages={295-324},
  year={2009},
}
Yves Cornulier, and Romain Tessera. Contracting automorphisms and$L$^{$p$}-cohomology in degree one. 2009. Vol. 49. In Arkiv for Matematik. pp.295-324. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203630465775003.
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