Automorphisms of a Clifford-like parallelism

Abstract

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 Γ ℓ 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 Γ ℓ or coincides with Γ ℓ even though ∥ ≠ ∥ ℓ .