KMS Of Academy of mathematics and systems sciences, CAS
Generalized Poisson brackets and Lie algebras of type H in characteristic 0 | |
Osborn, JM; Zhao, KM | |
1999 | |
Source Publication | MATHEMATISCHE ZEITSCHRIFT |
ISSN | 0025-5874 |
Volume | 230Issue:1Pages:107-143 |
Abstract | 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. |
Language | 英语 |
WOS Research Area | Mathematics |
WOS Subject | Mathematics |
WOS ID | WOS:000078270200006 |
Publisher | SPRINGER VERLAG |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/14382 |
Collection | 中国科学院数学与系统科学研究院 |
Corresponding Author | Osborn, JM |
Affiliation | 1.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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