Generalized Clifford parallelisms
Andrea Blunck,Stefano Pasotti,Silvia Pianta +2 more
- Vol. 11, Iss: 11, pp 197-212
TLDR
Generalized Clifford parallelisms involving hyperbolic quadrics in projective spaces over suitable quadratic extensions of F are defined with the help of a quaternion skew field H over a field F of arbitrary characteristic.Abstract:
We define generalized Clifford parallelisms in PG ( 3 , F ) with the help of a quaternion skew field H over a field F of arbitrary characteristic. Moreover we give a geometric description of such parallelisms involving hyperbolic quadrics in projective spaces over suitable quadratic extensions of F .read more
Citations
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Book ChapterDOI
An Inventory of Moufang Polygons
Jacques Tits,Richard M. Weiss +1 more
TL;DR: In Part III of this book, it is proved that every Moufang polygon is isomorphic to one of the Moufag polygons described in this chapter.
Journal ArticleDOI
Clifford parallelism: old and new definitions, and their use
Dieter Betten,Rolf Riesinger +1 more
TL;DR: In this paper, the concept of Clifford parallelism was introduced, which consists of all regular spreads of the real projective 3-space whose focal lines form a regulus contained in an imaginary quadric (D1 = Klein's definition).
Journal ArticleDOI
A note on Clifford parallelisms in characteristic two
TL;DR: In this article, it is shown that a purely inseparable field extension L/F with some extra property and degree [L : F] = 4 determines a Clifford parallelism on the set of lines of the three-dimensional projective space over F.
Journal ArticleDOI
Pencilled regular parallelisms
Hans Havlicek,Rolf Riesinger +1 more
TL;DR: In this article, the existence of pencilled line sets with respect to the Klein quadric was shown to be an algebraic condition for hyperflock determining line sets (hfd line sets).
Journal ArticleDOI
Clifford parallelisms defined by octonions
TL;DR: In this paper, the authors define (left and right) Clifford parallelisms on a seven-dimensional projective space algebraically, using an octonion division algebra, and determine the automorphism groups of these parallelisms.
References
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Book
Quadratic and Hermitian Forms
TL;DR: In this article, the authors present a classification of Quadratic Forms over Fields and their application in Fields of Prescribed Level, including the following: 1. Symmetric Bilinear Forms over Dedekind rings and Global Fields.
Book
Projective and Polar Spaces
TL;DR: In this article, the authors show that the Desarguesian spread theorem can be expressed as a combination of the following: 1, 9, 28, 28 affine plane, 18, 35 affine space, 3, 6 algebraic curve, 47 algebraic variety, 47 alternating bilinear form, 73 alternating groups, 120 alternative division rings, 104 anisotropic, 79 anti-automorphism, 2 atom, 34 atomic lattice, 34 automorphism, 15 axis, 55 Baer subplane, 128 biliné form, 72 binary Golay