非阶化Witt代数的一阶上同调群

发布时间：2018-05-02 15:36

  本文选题：Witt代数 + 非阶化Witt代数　； 参考：《上海师范大学》2017年硕士论文

【摘要】：无限维李代数上同调是李代数的重要研究对象.上世纪九十年代，Lou研究理论物理的广义对称性时得到了非阶化Witt代数W[14].由于非阶化Witt代数W本身结构更复杂，，使得对它的结构和表示的研究比Witt代数更为困难.本文生要研究无限维非阶化Witt代数W系数在张量模Fα',a,b中的一阶上同调群.在同构意义下，我们得到了如下的结果:其中线性映射D1,D2,D3定义如下：D0(L_(α,m))=αV_(α,m)+mV_(α,m-1),D1(L_(α,m))=α~2V_(α,m)+2mαV_(α,m-1)+m(m-1)V_(α,m-3)2,D2(L_(α,m))=α~3V_(α,m)+3mα~2V_(α,m-1)+3αm(m-1)V_(α,m-3)2+m(m-1)(m-2)V_(α,m-3)3,任意α,m ∈ Z.
[Abstract]:Cohomology of infinite dimensional lie algebras is an important research object of lie algebras. In the 1990s, when he studied the generalized symmetry of theoretical physics, he obtained the nongraded Witt algebra W [14]. Due to the complexity of the structure of non-graded Witt algebra W itself, it is more difficult to study its structure and representation than that of Witt algebra. In this paper, we study the cohomology group of W coefficients in tensor modules F 伪 and a b in infinite dimensional nonhierarchical Witt algebras. 鍦ㄥ悓鏋勬剰涔変笅,鎴戜滑寰楀埌浜嗗�備笅鐨勭粨鏋�:鍏朵腑绾挎

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