
AFFINE SPINOR DECOMPOSITION IN THREEDIMENSIONAL AFFINE GEOMETRY
Chengran WU, Hongbo LI
Acta mathematica scientia,Series B. 2022, 42 (6):
23012335.
DOI: 10.1007/s1047302206079
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 threedimensional 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.
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