Algebraic groups over free and hyperbolic groups

Vincent Guirardel; Chloé Perin

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arXiv · 2506.21350

Algebraic groups over free and hyperbolic groups

Vincent Guirardel·Chloé Perin

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Abstract

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.

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Vincent Guirardel, Chloé Perin. 2025-06-26. Algebraic groups over free and hyperbolic groups. https://arxiv.org/abs/2506.21350

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