Generalized Poisson brackets and Lie algebras of type H in characteristic 0
文献类型：期刊论文
| 作者 | Osborn, JM; Zhao, KM |
| 刊名 | MATHEMATISCHE ZEITSCHRIFT
 |
| 出版日期 | 1999 |
| 卷号 | 230期号:1页码:107-143 |
| ISSN号 | 0025-5874 |
| 英文摘要 | 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. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000078270200006 |
| 出版者 | SPRINGER VERLAG |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/14381]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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