Infinite families of triangle presentations
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929477989171200 |
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| author | Loué, Alex |
| author_facet | Loué, Alex |
| contents | A triangle presentation is a combinatorial datum that encodes the action of a group on a $2$-dimensional triangle complex with prescribed links, which is simply transitive on the vertices. We provide the first infinite family of triangle presentations that give rise to lattices in exotic buildings of type $\widetilde{\text{A}_2}$ of arbitrarily large order. Our method also gives rise to infinite families of triangle presentations for other link types, such as opposition complexes in Desarguesian projective planes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_15763 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Infinite families of triangle presentations Loué, Alex Group Theory Combinatorics 20F65 (Primary) 51E24, 11F06 (Secondary) A triangle presentation is a combinatorial datum that encodes the action of a group on a $2$-dimensional triangle complex with prescribed links, which is simply transitive on the vertices. We provide the first infinite family of triangle presentations that give rise to lattices in exotic buildings of type $\widetilde{\text{A}_2}$ of arbitrarily large order. Our method also gives rise to infinite families of triangle presentations for other link types, such as opposition complexes in Desarguesian projective planes. |
| title | Infinite families of triangle presentations |
| topic | Group Theory Combinatorics 20F65 (Primary) 51E24, 11F06 (Secondary) |
| url | https://arxiv.org/abs/2408.15763 |