Geometry of 2 x 2 hermitian matrices

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	Geometry of 2 x 2 hermitian matrices
	Huang, LP ; Wan, ZX
	2002-08-01
发表期刊	SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY
ISSN	1006-9283
卷号	45 期号:8 页码:1025-1037
摘要	Let D be a division ring which possesses an involution a --> (a) over bar. Assume that F = {a is an element of D\a = (a) over bar} is a proper subfield of D and is contained in the center of D. It is pointed out that if D is of characteristic not two, D is either a separable quadratic extension of F or a division ring of generalized quaternions over F and that if D is of characteristic two, D is a separable quadratic extension of F. Thus the trace map Tr: D --> F, a --> a + (a) over bar is always surjective, which is formerly posed as an assumption in the fundamental theorem of n x n hermitian matrices over D when n greater than or equal to 3 and now can be deleted. When D is a field, the fundamental theorem of 2 x 2 hermitian matrices over D has already been proved. This paper proves the fundamental theorem of 2 x 2 hermitian matrices over any division ring of generalized quaternions of characteristic not two.
关键词	division ring involution generalized quaternion hermitian matrix adjacency
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000177545600009
出版者	SCIENCE CHINA PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/17508
专题	中国科学院数学与系统科学研究院
通讯作者	Huang, LP
作者单位	1.Xiangtan Polytech Univ, Inst Math, Xiangtan 411201, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China 3.Nankai Univ, Ctr Combinator, Tianjin 300071, Peoples R China
推荐引用方式 GB/T 7714	Huang, LP,Wan, ZX. Geometry of 2 x 2 hermitian matrices[J]. SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY,2002,45(8):1025-1037.
APA	Huang, LP,&Wan, ZX.(2002).Geometry of 2 x 2 hermitian matrices.SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY,45(8),1025-1037.
MLA	Huang, LP,et al."Geometry of 2 x 2 hermitian matrices".SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY 45.8(2002):1025-1037.