Real division algebras with large automorphism group
文献类型：期刊论文
| 作者 | Dokovic, DZ; Zhao, KM |
| 刊名 | JOURNAL OF ALGEBRA
 |
| 出版日期 | 2004-12-15 |
| 卷号 | 282期号:2页码:758-796 |
| ISSN号 | 0021-8693 |
| DOI | 10.1016/j.jalgebra.2004.03.016 |
| 英文摘要 | 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. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000225308100012 |
| 出版者 | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/824]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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