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单扩张型Lie Rinehart代数的分类定理
引用本文:张黎明,加羊杰,陈酌.单扩张型Lie Rinehart代数的分类定理[J].纯粹数学与应用数学,2008,24(2).
作者姓名:张黎明  加羊杰  陈酌
作者单位:1. 青海师范大学民族师范学院,青海,西宁,810008
2. 首都师范大学数学科学学院,北京,100037
3. 北京大学数学系,北京,100871
基金项目:北京市教育委员会科技民展计划面上项目
摘    要:定义单扩张型Lie Rinehart代数,从而给出一种通过导子构造Lie Rinehart代数的途径.指出这是一种特殊的作用Lie Rinehart代数.在系数环是没有零因子的交换代数的前提下,给出单扩张型Lie Rinehart代数的完全分类定理.特别的,证明多项式环上的任何非平凡作用Lie Rinehart代数必然是单扩张型的,并给出其标准型.

关 键 词:Lie  Rinehart代数  导子  单扩张型代数

Simple extended Lie Rinehart algebras and their classifications
ZHANG Li-ming,JIA Yang-jie,CHEN Zhuo.Simple extended Lie Rinehart algebras and their classifications[J].Pure and Applied Mathematics,2008,24(2).
Authors:ZHANG Li-ming  JIA Yang-jie  CHEN Zhuo
Institution:ZHANG Li-ming~1 JIA Yang-jie~2 CHEN Zhuo~3 1.Department of Mathematics,Nationalities College of Qinghal Normal University,Xining 810008,China,2.Department of Mathematics,Capital Normal University,Beijing 100800,3.Department of Mathematics,Peking University,Beijing 100871
Abstract:The notion of a simple extended Lie Rinehart algebra is defined and this gives a way to construct Lie Rinehart algebras via derivations.It is a special kind of the action Lie Rinehart algebras.Under the condition that the coefficient ring is a commutative algbra and has no zero-divizors,the full classifaction of such simple extended Lie Rinehart algebras is given.For the action Lie Rinehart algebras which arise from nontrivial actions on the ring of polynomials,it is proved that they must be simple extended...
Keywords:Lie Rinehart algebra  derivation  simple extension  
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