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.
Funding statement: The second author was partially supported by GNSAGA of INdAM (Italy). The third author was partially supported by Università Cattolica del Sacro Cuore (Milano, Italy) in the framework of Call D.1 2018.
Communicated by: R. Löwen
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