AFFINE SPINOR DECOMPOSITION IN THREE-DIMENSIONAL AFFINE GEOMETRY

Spin group and screw algebra,as extensions of quaternions and vector algebra,respectively,have important applications in geometry,physics and engineering.In three-dimensional projective geometry,when acting on lines,each projective transformation can be decomposed into at most three harmonic project...

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Bibliographic Details
Published in数学物理学报（英文版） Vol. 42; no. 6; pp. 2301 - 2335
Main Authors Chengran WU, Hongbo LI
Format Journal Article
LanguageEnglish
Published Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China%Academy of Mathematics and Systems Science,University of Chinese Academy of Sciences,Chinese Academy of Sciences,Beijing 100190,China 2022
Subjects
spin group
line geometry
affine line reflection
spinor decomposition
affine transformation
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ISSN0252-9602
DOI10.3969/j.issn.0252-9602.2022.06.008

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Summary:Spin group and screw algebra,as extensions of quaternions and vector algebra,respectively,have important applications in geometry,physics and engineering.In three-dimensional projective geometry,when acting on lines,each projective transformation can be decomposed into at most three harmonic projective reflections with respect to projective lines,or equivalently,each projective spinor can be decomposed into at most three orthogonal Minkowski bispinors,each inducing a harmonic projective line reflection.In this paper,we establish the corresponding result for three-dimensional affine geometry:with each affine transformation is found a minimal decomposition into general affine reflections,where the number of general affine reflections is at most three;equivalently,each affine spinor can be decomposed into at most three affine Minkowski bispinors,each inducing a general affine line reflection.
ISSN:0252-9602
DOI:10.3969/j.issn.0252-9602.2022.06.008