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...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
| Published: |
Association des Annales de l'institut Fourier
2015
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| Summary: | 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. |
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