Automorphisms of a Clifford-like parallelism

Stefano Pasotti; Silvia Pianta; Hans Havlicek

doi:10.1515/advgeom-2020-0027

Automorphisms of a Clifford-like parallelism

Stefano Pasotti, Silvia Pianta, Hans Havlicek

Università Cattolica del Sacro Cuore

Research output: Contribution to journal › Article

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 ∥.

Original language	English
Pages (from-to)	63-73
Number of pages	11
Journal	Advances in Geometry
Volume	21
DOIs	https://doi.org/10.1515/advgeom-2020-0027
Publication status	Published - 2021

Keywords

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

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10.1515/advgeom-2020-0027

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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 ∥.",

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T1 - Automorphisms of a Clifford-like parallelism

AU - Pasotti, Stefano

AU - Pianta, Silvia

AU - Havlicek, Hans

PY - 2021

Y1 - 2021

N2 - 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 ∥.

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 -

Automorphisms of a Clifford-like parallelism

Abstract

Keywords

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