Some remarks on Spin-orbits of unit vectors
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909240044552192 |
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| author | Syed, Tariq |
| author_facet | Syed, Tariq |
| contents | For $n \in \mathbb{N}$ and a commutative ring $R$ with $2 \in R^{\times}$, the group $SL_n (R)$ acts on the set $Um_n (R)$ of unimodular vectors of length $n$ and $Spin_{2n}(R)$ acts on the set of unit vectors $U_{2n-1}(R)$. We give an example of a ring for which the comparison map $Um_n (R)/SL_n (R) \rightarrow U_{2n-1}(R)/Spin_{2n}(R)$ fails to be bijective. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_11120 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Some remarks on Spin-orbits of unit vectors Syed, Tariq Algebraic Geometry Commutative Algebra K-Theory and Homology For $n \in \mathbb{N}$ and a commutative ring $R$ with $2 \in R^{\times}$, the group $SL_n (R)$ acts on the set $Um_n (R)$ of unimodular vectors of length $n$ and $Spin_{2n}(R)$ acts on the set of unit vectors $U_{2n-1}(R)$. We give an example of a ring for which the comparison map $Um_n (R)/SL_n (R) \rightarrow U_{2n-1}(R)/Spin_{2n}(R)$ fails to be bijective. |
| title | Some remarks on Spin-orbits of unit vectors |
| topic | Algebraic Geometry Commutative Algebra K-Theory and Homology |
| url | https://arxiv.org/abs/2308.11120 |