Automorphisms of a Clifford-like parallelism

Silvia Pianta; Stefano Pasotti; Hans Havlicek

doi:10.1515/advgeom-2020-0027

Automorphisms of a Clifford-like parallelism

Silvia Pianta, Stefano Pasotti, Hans Havlicek

Risultato della ricerca: Contributo in rivista › Articolo in rivista

Abstract

We focus on the description of the automorphism group Γ∥ of a Clifford-like parallelism ∥ on a 3-dimensional projective double space ((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 ∥.

Lingua originale	English
pagine (da-a)	63-73
Numero di pagine	11
Rivista	Advances in Geometry
Volume	21
DOI	https://doi.org/10.1515/advgeom-2020-0027
Stato di pubblicazione	Pubblicato - 2021

Keywords

Clifford parallelism
Clifford-like parallelism
automorphism
projective double space
quaternion skew field

Accesso al documento

10.1515/advgeom-2020-0027

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AU - Pianta, Silvia

AU - Pasotti, Stefano

AU - Havlicek, Hans

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AB - We focus on the description of the automorphism group Γ∥ of a Clifford-like parallelism ∥ on a 3-dimensional projective double space ((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 ∥.

KW - Clifford parallelism

KW - Clifford-like parallelism

KW - automorphism

KW - projective double space

KW - quaternion skew field

KW - Clifford parallelism

KW - Clifford-like parallelism

KW - automorphism

KW - projective double space

KW - quaternion skew field

UR - http://hdl.handle.net/10807/176599

U2 - 10.1515/advgeom-2020-0027

DO - 10.1515/advgeom-2020-0027

M3 - Article

VL - 21

SP - 63

EP - 73

JO - Advances in Geometry

JF - Advances in Geometry

SN - 1615-715X

ER -