Generalized Poisson brackets and Lie algebras of type H in characteristic 0

CSpace

	Generalized Poisson brackets and Lie algebras of type H in characteristic 0
	Osborn, JM ; Zhao, KM
	1999
发表期刊	MATHEMATISCHE ZEITSCHRIFT
ISSN	0025-5874
卷号	230 期号:1 页码:107-143
摘要	The Lie algebra of Cartan type H which occurs as a subalgebra of the Lie algebra of derivations of the polynomial algebra F[x(1),...,x(n),x(-1),...,x(-n)] was generalized by the first author to a class which included a subalgebra of the derivations of the Laurent polynomials F[x(1),...,x(n),x(-1),...,x(-n, )x(1)(-1),...,x(n)(-1),x(-1)(-1),...,x(-n)(-1)]. We show in this paper that these generalizations of Cartan type H algebras are isomorphic to certain generalizations of the classical algebra of Poisson brackets, and that it can be generalized further. In turn, these algebras can be recast in a form that is an adaption of a class of Lie algebras of characteristic p that was defined in 1958 be R. Block. A further generalization of these algebras is the main topic of this paper. We show when these algebras are simple, find their derivations, and determine all possible isomorphisms between two of these algebras. Mathematics Subject Classification (1991): 17B40, 17B65, 17B66, 17B68, 17B70.
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000078270200006
出版者	SPRINGER VERLAG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/14382
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. Generalized Poisson brackets and Lie algebras of type H in characteristic 0[J]. MATHEMATISCHE ZEITSCHRIFT,1999,230(1):107-143.
APA	Osborn, JM,&Zhao, KM.(1999).Generalized Poisson brackets and Lie algebras of type H in characteristic 0.MATHEMATISCHE ZEITSCHRIFT,230(1),107-143.
MLA	Osborn, JM,et al."Generalized Poisson brackets and Lie algebras of type H in characteristic 0".MATHEMATISCHE ZEITSCHRIFT 230.1(1999):107-143.