Orthogonal forms of Kac–Moody groups are acylindrically hyperbolic
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...
| প্রধান লেখক: | , |
|---|---|
| বিন্যাস: | Journal article |
| ভাষা: | English |
| প্রকাশিত: |
Association des Annales de l'institut Fourier
2015
|
| সংক্ষিপ্ত: | 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. |
|---|