AFFINE SPINOR DECOMPOSITION IN THREE-DIMENSIONAL AFFINE GEOMETRY  

作　　者：Chengran WU Hongbo LI 吴澄冉;李洪波(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)

机构地区：[1]Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China [2]Academy of Mathematics and Systems Science,University of Chinese Academy of Sciences,Chinese Academy of Sciences,Beijing 100190,China

出　　处：《Acta Mathematica Scientia》2022年第6期2301-2335,共35页数学物理学报（B辑英文版）

基　　金：Supported partially by National Key Research and Development Project(2020YFA0712300)。

摘　　要：Spin group and screw algebra,as extensions of quaternions and vector algebra,respectively,have important applications in geometry,physics and engineering.In threedimensional 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.

关 键 词：spin group spinor decomposition affine transformation line geometry afine line reflection 

分 类 号：O152.5[理学—数学]