Algebraic groups over free and hyperbolic groups
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866914468163747840 |
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| author | Guirardel, Vincent Perin, Chloé |
| author_facet | Guirardel, Vincent Perin, Chloé |
| contents | We define an algebraic group over a group $G$ to be a variety - that is, a subset of $G^d$ defined by equations over $G$ - endowed with a group law whose coordinates can be expressed as word maps. In the case where $G$ is a torsion-free hyperbolic group and the underlying variety is irreducible we give a complete description of all algebraic groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_21350 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Algebraic groups over free and hyperbolic groups Guirardel, Vincent Perin, Chloé Group Theory Algebraic Geometry 20F67, 20F65, 20G99, 14L10 We define an algebraic group over a group $G$ to be a variety - that is, a subset of $G^d$ defined by equations over $G$ - endowed with a group law whose coordinates can be expressed as word maps. In the case where $G$ is a torsion-free hyperbolic group and the underlying variety is irreducible we give a complete description of all algebraic groups. |
| title | Algebraic groups over free and hyperbolic groups |
| topic | Group Theory Algebraic Geometry 20F67, 20F65, 20G99, 14L10 |
| url | https://arxiv.org/abs/2506.21350 |