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Generalized Poisson brackets and Lie algebras of type H in characteristic 0
Osborn, JM; Zhao, KM
1999
Source PublicationMATHEMATISCHE ZEITSCHRIFT
ISSN0025-5874
Volume230Issue:1Pages:107-143
AbstractThe 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.
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000078270200006
PublisherSPRINGER VERLAG
Citation statistics
Cited Times:15[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/14382
Collection中国科学院数学与系统科学研究院
Affiliation1.Univ Wisconsin, Dept Math, Madison, WI 53706 USA
2.Acad Sinica, Inst Syst Sci, Beijing 100080, Peoples R China
Recommended Citation
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.
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