Rank-One Isometries of Buildings and Quasi-Morphisms of Kac–Moody Groups

被引：0

作者：

Pierre-Emmanuel Caprace

Koji Fujiwara

机构：

[1] Université Catholique de Louvain,Graduate School of Information Science

[2] Tohoku University,undefined

来源：

Geometric and Functional Analysis | 2010年 / 19卷

关键词：

Kac-Moody group; building; rank-one isometry; quasi-morphism; commutator length; 20F65; 20E42; 20E32; 22E65;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

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 in particular 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 [MK, Prob. 14.13]. 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.

引用

页码：1296 / 1319

页数：23

共 32 条

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