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...
| मुख्य लेखकों: | , |
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| स्वरूप: | Journal article |
| भाषा: | English |
| प्रकाशित: |
Association des Annales de l'institut Fourier
2015
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| _version_ | 1826288803528048640 |
|---|---|
| author | Caprace, P Hume, D |
| author_facet | Caprace, P Hume, D |
| author_sort | Caprace, P |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T02:19:13Z |
| format | Journal article |
| id | oxford-uuid:a35454ff-a70a-4f5b-a4fd-d755e9dff0f2 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T02:19:13Z |
| publishDate | 2015 |
| publisher | Association des Annales de l'institut Fourier |
| record_format | dspace |
| spelling | oxford-uuid:a35454ff-a70a-4f5b-a4fd-d755e9dff0f22022-03-27T02:26:10ZOrthogonal forms of Kac–Moody groups are acylindrically hyperbolicJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:a35454ff-a70a-4f5b-a4fd-d755e9dff0f2EnglishSymplectic Elements at OxfordAssociation des Annales de l'institut Fourier2015Caprace, PHume, DWe 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. |
| spellingShingle | Caprace, P Hume, D Orthogonal forms of Kac–Moody groups are acylindrically hyperbolic |
| title | Orthogonal forms of Kac–Moody groups are acylindrically hyperbolic |
| title_full | Orthogonal forms of Kac–Moody groups are acylindrically hyperbolic |
| title_fullStr | Orthogonal forms of Kac–Moody groups are acylindrically hyperbolic |
| title_full_unstemmed | Orthogonal forms of Kac–Moody groups are acylindrically hyperbolic |
| title_short | Orthogonal forms of Kac–Moody groups are acylindrically hyperbolic |
| title_sort | orthogonal forms of kac moody groups are acylindrically hyperbolic |
| work_keys_str_mv | AT capracep orthogonalformsofkacmoodygroupsareacylindricallyhyperbolic AT humed orthogonalformsofkacmoodygroupsareacylindricallyhyperbolic |