Generalized affine buildings for semisimple algebraic groups over real closed fields
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908750235828224 |
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| author | Appenzeller, Raphael |
| author_facet | Appenzeller, Raphael |
| contents | We use real algebraic geometry to construct an affine $Λ$-building $B$ associated to the $\mathbb{F}$-points of a semisimple algebraic group, where $\mathbb{F}$ is a valued real closed field. We characterize the spherical building at infinity and the local building at a base point. We compute stabilizers of various subsets of $B$ and obtain group decompositions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_03226 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Generalized affine buildings for semisimple algebraic groups over real closed fields Appenzeller, Raphael Group Theory Geometric Topology 51E24, 20G25, 14P10, 12J25 We use real algebraic geometry to construct an affine $Λ$-building $B$ associated to the $\mathbb{F}$-points of a semisimple algebraic group, where $\mathbb{F}$ is a valued real closed field. We characterize the spherical building at infinity and the local building at a base point. We compute stabilizers of various subsets of $B$ and obtain group decompositions. |
| title | Generalized affine buildings for semisimple algebraic groups over real closed fields |
| topic | Group Theory Geometric Topology 51E24, 20G25, 14P10, 12J25 |
| url | https://arxiv.org/abs/2601.03226 |