Affine Spinor Decomposition in Three-Dimensional Affine Geometry

doi:10.1007/s10473-022-0607-9

	Affine Spinor Decomposition in Three-Dimensional Affine Geometry
	Wu, Chengran 1; Li, Hongbo 2
刊名	ACTA MATHEMATICA SCIENTIA
	2022-08-30
页码	35
关键词	spin group spinor decomposition affine transformation line geometry affine line reflection
ISSN号	0252-9602
DOI	10.1007/s10473-022-0607-9
英文摘要	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.
资助项目	National Key Research and Development Project[2020YFA0712300]
WOS研究方向	Mathematics
语种	英语
出版者	SPRINGER
WOS记录号	WOS:000847649200008
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/61056]
专题	中国科学院数学与系统科学研究院
通讯作者	Li, Hongbo
作者单位	1.Acad Math & Syst Sci, Chinese Acad Sci, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Acad Math & Syst Sci, Chinese Acad Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Wu, Chengran,Li, Hongbo. Affine Spinor Decomposition in Three-Dimensional Affine Geometry[J]. ACTA MATHEMATICA SCIENTIA,2022:35.
APA	Wu, Chengran,&Li, Hongbo.(2022).Affine Spinor Decomposition in Three-Dimensional Affine Geometry.ACTA MATHEMATICA SCIENTIA,35.
MLA	Wu, Chengran,et al."Affine Spinor Decomposition in Three-Dimensional Affine Geometry".ACTA MATHEMATICA SCIENTIA (2022):35.