Rational Jordan decomposition of bilinear forms

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	Rational Jordan decomposition of bilinear forms
	Dokovic, DZ ; Zhao, KM
	2005-12-01
发表期刊	COMMUNICATIONS IN CONTEMPORARY MATHEMATICS
ISSN	0219-1997
卷号	7 期号:6 页码:769-786
摘要	This is a continuation of our previous work on Jordan decomposition of bilinear forms over algebraically closed fields of characteristic 0. In this note, we study Jordan decomposition of bilinear forms over any field K-0 of characteristic 0. Let V-0 be an n-dimensional vector space over K-0. Denote by B-0 the space of bilinear forms f : V-0 x V-0 -> K-0. We say that f = g + h, where f, g, h epsilon B-0, is a rational Jordan decomposition of f if, after extending the field K-0 to an algebraic closure K, we obtain a Jordan decomposition over K. By using the Galois group of K/K-0, we prove the existence of rational Jordan decompositions and describe a method for constructing all such decompositions. Several illustrative examples of rational Jordan decompositions of bilinear forms are included. We also show how to classify the unimodular congruence classes of bilinear forms over an algebraically closed field of characteristic different from 2 and over the real field.
关键词	bilinear form rational Jordan decomposition nilpotent orbit semi-simple orbit congruence class
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000234812200003
出版者	WORLD SCIENTIFIC PUBL CO PTE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/1379
专题	中国科学院数学与系统科学研究院
通讯作者	Zhao, KM
作者单位	1.Wilfrid Laurier Univ, Dept Math, Waterloo, ON N2L 3C5, Canada 2.Univ Waterloo, Dept Pure Math, Waterloo, ON N2L 3G1, Canada 3.Chinese Acad Sci, Inst Math, Acad Math & Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Dokovic, DZ,Zhao, KM. Rational Jordan decomposition of bilinear forms[J]. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS,2005,7(6):769-786.
APA	Dokovic, DZ,&Zhao, KM.(2005).Rational Jordan decomposition of bilinear forms.COMMUNICATIONS IN CONTEMPORARY MATHEMATICS,7(6),769-786.
MLA	Dokovic, DZ,et al."Rational Jordan decomposition of bilinear forms".COMMUNICATIONS IN CONTEMPORARY MATHEMATICS 7.6(2005):769-786.