类克利福德平行性的自同构
Automorphisms of a Clifford-like parallelism
AI总结：
研究四元数体上三维射影双空间中类克利福德平行性的自同构群，对比其与左平行性自同构群的关系，构造实例说明不同四元数体下两类自同构群的包含或相等情形。
摘要：
本文聚焦于刻画四元数体$H$（其中心为任意特征的域$F$）上$3$维射影双空间$\bigl(\mathbb{P}(H_F),{\mathrel{\parallel_{\ell}}},{\mathrel{\parallel_{r}}}\bigr)$中类克利福德平行性$\parallel$的自同构群$Γ_{\parallel}$。我们将$Γ_{\parallel}$与左平行性$\mathrel{\parallel_{\ell}}$的自同构群$Γ_{\ell}$进行比较，二者与$\mathrm{Aut}(H)$密切相关。我们构建并讨论了若干实例，表明在某些四元数体上，可以选取$\parallel$使得$Γ_{\parallel}$真包含于$Γ_{\ell}$，或者即使满足${\parallel} \neq{\mathrel{\parallel_{\ell}}}$，$Γ_{\parallel}$也与$Γ_{\ell}$相等。
英文摘要：
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 ${\parallel} \neq{\mathrel{\parallel_{\ell}}}$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
