Invariant theory for non-associative real two-dimensional algebras and its applications

CSpace

	Invariant theory for non-associative real two-dimensional algebras and its applications
	Dokovic, D ; Zhao, KM
	2004-03-01
发表期刊	TRANSFORMATION GROUPS
ISSN	1083-4362
卷号	9 期号:1 页码:3-23
摘要	The set A of all non-associative algebra structures on a fixed 2-dimensional real vector space A is naturally a GL(2, R)-module. We compute the ring of SL(2, R)-invariants in the ring of polynomial functions, P, on A. We use invariant theory to compute the exact number of nonzero idempotents of an arbitrary 2-dimensional real division algebra. We show that the absolute invariants (i.e., the GL(2, R)-invariants in the field of fractions of P) distinguish the isomorphism classes of 2-dimensional non-associative real division algebras. We show that the (open) set Omega(+) subset of A of all division algebra structures on A has four connected components. A similar result is proved for another class of regular 2-dimensional real algebras (the principal isotopes of the algebra R circle plus R).
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000220251700001
出版者	BIRKHAUSER BOSTON INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/576
专题	中国科学院数学与系统科学研究院
通讯作者	Dokovic, D
作者单位	1.Univ Waterloo, Dept Pure Math, Waterloo, ON N2L 3G1, Canada 2.Chinese Acad Sci, Acad Math & Syst Sci, Math Inst, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Dokovic, D,Zhao, KM. Invariant theory for non-associative real two-dimensional algebras and its applications[J]. TRANSFORMATION GROUPS,2004,9(1):3-23.
APA	Dokovic, D,&Zhao, KM.(2004).Invariant theory for non-associative real two-dimensional algebras and its applications.TRANSFORMATION GROUPS,9(1),3-23.
MLA	Dokovic, D,et al."Invariant theory for non-associative real two-dimensional algebras and its applications".TRANSFORMATION GROUPS 9.1(2004):3-23.