Orthogonal forms of Kac–Moody groups are acylindrically hyperbolic

Author: 

Hume, D
Caprace, P

Publication Date: 

1 January 2015

Journal: 

Annales de l’institut Fourier

Last Updated: 

2020-01-22T17:28:10.473+00:00

Issue: 

6

Volume: 

65

DOI: 

10.5802/aif.2998

page: 

2613-2640

abstract: 

We give sufficient conditions for a group acting on a geodesic metric space to be acylindrically hyperbolic and mention various applications to groups acting on CAT(0) spaces. We prove that a group acting on an irreducible non-spherical non-affine building is acylindrically hyperbolic provided there is a chamber with finite stabiliser whose orbit contains an apartment. Finally, we show that the following classes of groups admit an action on a building with those properties: orthogonal forms of Kac–Moody groups over arbitrary fields, and irreducible graph products of arbitrary groups - recovering a result of Minasyan–Osin.

Symplectic id: 

672216

Submitted to ORA: 

Not Submitted

Publication Type: 

Journal Article