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Automorphisms of a Clifford-like parallelism

Hans Havlicek , Stefano Pasotti and Silvia Pianta EMAIL logo
From the journal Advances in Geometry


We focus on the description of the automorphism group Γ of a Clifford-like parallelism ∥ on a 3-dimensional projective double space (ℙ(HF), ∥, ∥r) over a quaternion skew field H (of any characteristic). We compare Γ with the automorphism group Γ of the left parallelism ∥, 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 or coincides with Γ even though ∥ ≠ ∥.

MSC 2010: 51A15; 51J15

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.

  1. Communicated by: R. Löwen


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Received: 2018-12-06
Revised: 2019-02-07
Published Online: 2021-01-22
Published in Print: 2021-01-27

© 2021 Walter de Gruyter GmbH, Berlin/Boston

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