Rank one isometries of buildings and quasi-morphisms of Kac-Moody groups
| dc.creator | Caprace, Pierre-Emmanuel | |
| dc.creator | Fujiwara, Koji | |
| dc.date | 2008-09-02 | |
| dc.date | 2009-04-28 | |
| dc.date.accessioned | 2026-07-07T13:08:39Z | |
| dc.date.available | 2026-07-07T13:08:39Z | |
| dc.description | Given 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.description | 19 pages; some typos have been corrected and the list of references updated | |
| dc.identifier | https://arxiv.org/abs/0809.0470 | |
| dc.identifier | http://arxiv.org/abs/0809.0470 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/228485 | |
| dc.subject | Group Theory | |
| dc.subject | 20F65; 20E42; 20E32; 22E65 | |
| dc.title | Rank one isometries of buildings and quasi-morphisms of Kac-Moody groups | |
| dc.type | text |