Automorphisms of a Clifford-like parallelism
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2019
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| _version_ | 1866910312782888960 |
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| author | Havlicek, Hans Pasotti, Stefano Pianta, Silvia |
| author_facet | Havlicek, Hans Pasotti, Stefano Pianta, Silvia |
| contents | In this paper we focus on the description of the automorphism group $Γ_{\parallel}$ of a Clifford-like parallelism $\parallel$ on a $3$-dimensional projective double space $\bigl(\mathbb{P}(H_F),{\mathrel{\parallel_{\ell}}},{\mathrel{\parallel_{r}}}\bigr)$ over a quaternion skew field $H$ (with centre a field $F$ of any characteristic). We compare $Γ_{\parallel}$ with the automorphism group $Γ_{\ell}$ of the left parallelism $\mathrel{\parallel_{\ell}}$, which is strictly related to $\mathrm{Aut}(H)$. We build up and discuss several examples showing that over certain quaternion skew fields it is possible to choose $\parallel$ in such a way that $Γ_{\parallel}$ is either properly contained in $Γ_{\ell}$ or coincides with $Γ_{\ell}$ even though ${\parallel} \neq{\mathrel{\parallel_{\ell}}}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1903_10331 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Automorphisms of a Clifford-like parallelism Havlicek, Hans Pasotti, Stefano Pianta, Silvia Algebraic Geometry 51A15, 51J15 In this paper we focus on the description of the automorphism group $Γ_{\parallel}$ of a Clifford-like parallelism $\parallel$ on a $3$-dimensional projective double space $\bigl(\mathbb{P}(H_F),{\mathrel{\parallel_{\ell}}},{\mathrel{\parallel_{r}}}\bigr)$ over a quaternion skew field $H$ (with centre a field $F$ of any characteristic). We compare $Γ_{\parallel}$ with the automorphism group $Γ_{\ell}$ of the left parallelism $\mathrel{\parallel_{\ell}}$, which is strictly related to $\mathrm{Aut}(H)$. We build up and discuss several examples showing that over certain quaternion skew fields it is possible to choose $\parallel$ in such a way that $Γ_{\parallel}$ is either properly contained in $Γ_{\ell}$ or coincides with $Γ_{\ell}$ even though ${\parallel} \neq{\mathrel{\parallel_{\ell}}}$. |
| title | Automorphisms of a Clifford-like parallelism |
| topic | Algebraic Geometry 51A15, 51J15 |
| url | https://arxiv.org/abs/1903.10331 |