A characterization of the block Lie algebra and its q-forms in characteristic 0
文献类型：期刊论文
| 作者 | Osborn, JM; Zhao, KM |
| 刊名 | JOURNAL OF ALGEBRA
 |
| 出版日期 | 1998-09-15 |
| 卷号 | 207期号:2页码:367-408 |
| ISSN号 | 0021-8693 |
| 英文摘要 | The Block algebra L referred to here is the Lie algebra over a field F of characteristic 0 with basis {e(r,s) \ (r, s) is an element of Z X Z \ {(0,0)}} and subject to the commutation relations [e(h,k), e(r,s)] = (rk - sh)e(h+r), (k+s). Let 0, 1 not equal q is an element of F. The q-form L(q) of L is the Lie algebra with basis {e(r,s)(q) \ ((r,s)) is an element of Z x Z \ {(0,0)}} and subject to the commutation relations [e(h,k)(q), e(r,s)(q)] = (q(rk) - q(sh))e(h+r, k+s)(q). We study here a Z x Z-graded Lie algebra A = + (i, j is an element of Z) A(i,j) with A(0,0) = 0 and dim A(i,j) less than or equal to 1 for all (i, j) is an element of Z X Z \ {(0, 0)}. In this paper, we show that A is necessarily isomorphic to L or L' (q) = [L(q), L(q)] for some g is an element of F if A satisfies a certain nondegeneracy condition. (C) 1998 Academic Press. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000076072800002 |
| 出版者 | ACADEMIC PRESS INC |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/13520]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Osborn, JM |
| 作者单位 | 1.Univ Wisconsin, Dept Math, Madison, WI 53706 USA 2.Acad Sinica, Inst Syst Sci, Beijing 100080, Peoples R China |
| 推荐引用方式 GB/T 7714 | Osborn, JM,Zhao, KM. A characterization of the block Lie algebra and its q-forms in characteristic 0[J]. JOURNAL OF ALGEBRA,1998,207(2):367-408. |
| APA | Osborn, JM,&Zhao, KM.(1998).A characterization of the block Lie algebra and its q-forms in characteristic 0.JOURNAL OF ALGEBRA,207(2),367-408. |
| MLA | Osborn, JM,et al."A characterization of the block Lie algebra and its q-forms in characteristic 0".JOURNAL OF ALGEBRA 207.2(1998):367-408. |
入库方式： OAI收割
来源：数学与系统科学研究院
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