Abstract We focus on the description of the automorphism group Γ∥ of a Clifford-like parallelism ∥ on a 3-dimensional projective double space (ℙ(HF), ∥ℓ, ∥r) over a quaternion skew field H (of any characteristic). We compare Γ∥ with the automorphism group Γℓ of the left parallelism ∥ℓ, which is strictly related to Aut(H). We build up and discuss several examples showing that over certain quaternion skew fields it is possible to choose ∥ in such a way that Γ∥ is either properly contained in Γℓ or coincides with Γℓ even though ∥ ≠ ∥ℓ.

中文翻译：

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类 Clifford 并行性的自同构

摘要 我们关注在四元数斜场 H（具有任何特征）上的三维射影双空间（ℙ(HF), ∥ℓ, ∥r) 上的类 Clifford 并行性 ∥ 的自同构群 Γ∥ 的描述. 我们将Γ∥与左并行∥ℓ的自同构群Γℓ进行比较，后者与Aut(H)严格相关。我们建立并讨论了几个例子，表明在某些四元数倾斜场上，可以选择 ∥ 使得 Γ∥ 要么正确包含在 Γℓ 中，要么与 Γℓ 重合，即使 ∥ ≠ ∥ℓ。