automorphisms of a clifford like parallelism

• DOI: 10.48550/arxiv.1903.10331
• Publication Date: 2021-01-01
• Authors: Pasotti, Stefano; Havlicek Hans; Pianta, Silvia
• Keywords: automorphism; quaternion skew field; clifford parallelism, automorphism, quaternion skew field; Clifford parallelism; 01 natural sciences; Mathematics - Algebraic Geometry; 51A15, 51J15; Clifford-like parallelism; projective double space; FOS: Mathematics; 0101 mathematics; Algebraic Geometry (math.AG)

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 .