Real division algebras with large automorphism group

doi:10.1016/j.jalgebra.2004.03.016

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	Real division algebras with large automorphism group
	Dokovic, DZ ; Zhao, KM
	2004-12-15
发表期刊	JOURNAL OF ALGEBRA
ISSN	0021-8693
卷号	282 期号:2 页码:758-796
摘要	We continue the study of the 8-dimensional real division algebras whose derivation algebra is large (of type G(2), A(2), 2A(1), or A(1)) begun by Benkart and Osborn in the early 1980s. For some of the families of real algebras that they constructed, we find necessary and sufficient conditions for them to be division algebras, determine when two division algebras in such a family are isomorphic or determine the automorphism group of such an algebra. We use one of these families to prove that every 2-dimensional real division algebra embeds in a 4-dimensional and in an 8-dimensional real division algebra. A new family, F-6, of non-isomorphic real 8-dimensional algebras, parametrized by the Euclidean space R-6, is constructed and studied in detail. The division algebras in F-6 correspond to a non-empty open subset of the parameter space. We also introduce an interesting 2-parameter subfamily. F-2 subset of F-6, which contains the generalized pseudo-octonion algebras. We obtain necessary and sufficient conditions for (A, mu) is an element of F-2 to be a division algebra. In the generic case, the algebras in F-6 are 1-generated and have SO(3) as the automorphism group. We also determine all (1-, 2-, and 4-dimensional) subalgebras of the division algebras in F-6. We show that there exist 8-dimensional (and 4-dimensional) real division algebras having a 1-dimensional subalgebra not contained in any 2-dimensional subalgebra. We also construct 8-dimensional real division algebras having a 2-dimensional subalgebra not contained in any 4-dimensional subalgebra. (C) 2004 Elsevier Inc. All rights reserved.
DOI	10.1016/j.jalgebra.2004.03.016
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000225308100012
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/825
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, Acad Math & Syst Sci, Inst Math, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Dokovic, DZ,Zhao, KM. Real division algebras with large automorphism group[J]. JOURNAL OF ALGEBRA,2004,282(2):758-796.
APA	Dokovic, DZ,&Zhao, KM.(2004).Real division algebras with large automorphism group.JOURNAL OF ALGEBRA,282(2),758-796.
MLA	Dokovic, DZ,et al."Real division algebras with large automorphism group".JOURNAL OF ALGEBRA 282.2(2004):758-796.