Rank one isometries of buildings and quasi-morphisms of Kac-Moody groups

dc.creatorCaprace, Pierre-Emmanuel
dc.creatorFujiwara, Koji
dc.date2008-09-02
dc.date2009-04-28
dc.date.accessioned2026-07-07T13:08:39Z
dc.date.available2026-07-07T13:08:39Z
dc.descriptionGiven an irreducible non-spherical non-affine (possibly non-proper) building $X$, we give sufficient conditions for a group $G < \Aut(X)$ to admit an infinite-dimensional space of non-trivial quasi-morphisms. The result applies to all irreducible (non-spherical and non-affine) Kac-Moody groups over integral domains. In particular, we obtain finitely presented simple groups of infinite commutator width, thereby answering a question of Valerii G. Bardakov from the Kourovka notebook. Independently of these considerations, we also include a discussion of rank one isometries of proper CAT(0) spaces from a rigidity viewpoint. In an appendix, we show that any homogeneous quasi-morphism of a locally compact group with integer values is continuous.
dc.description19 pages; some typos have been corrected and the list of references updated
dc.identifierhttps://arxiv.org/abs/0809.0470
dc.identifierhttp://arxiv.org/abs/0809.0470
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/228485
dc.subjectGroup Theory
dc.subject20F65; 20E42; 20E32; 22E65
dc.titleRank one isometries of buildings and quasi-morphisms of Kac-Moody groups
dc.typetext

Files

Collections