Twisted forms of classical groups
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866917465109299200 |
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| author | Voronetsky, Egor |
| author_facet | Voronetsky, Egor |
| contents | We give a unified description of twisted forms of classical reductive groups schemes. Such group schemes are constructed from algebraic objects of finite rank, excluding some exceptions of small rank. These objects, augmented odd form algebras, consist of $2$-step nilpotent groups with an action of the underlying commutative ring, hence we develop basic descent theory for them. In addition, we describe classical isotropic reductive groups as odd unitary groups up to an isogeny. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2004_08627 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Twisted forms of classical groups Voronetsky, Egor Group Theory Representation Theory 14L35 We give a unified description of twisted forms of classical reductive groups schemes. Such group schemes are constructed from algebraic objects of finite rank, excluding some exceptions of small rank. These objects, augmented odd form algebras, consist of $2$-step nilpotent groups with an action of the underlying commutative ring, hence we develop basic descent theory for them. In addition, we describe classical isotropic reductive groups as odd unitary groups up to an isogeny. |
| title | Twisted forms of classical groups |
| topic | Group Theory Representation Theory 14L35 |
| url | https://arxiv.org/abs/2004.08627 |