A characterization of the block Lie algebra and its q-forms in characteristic 0

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	A characterization of the block Lie algebra and its q-forms in characteristic 0
	Osborn, JM ; Zhao, KM
	1998-09-15
发表期刊	JOURNAL OF ALGEBRA
ISSN	0021-8693
卷号	207 期号:2 页码:367-408
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.
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000076072800002
出版者	ACADEMIC PRESS 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/13521
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.