本文選題：Witt代數 + 非階化Witt代數　； 參考：《上海師范大學》2017年碩士論文

【摘要】：無限維李代數上同調是李代數的重要研究對象.上世紀九十年代，Lou研究理論物理的廣義對稱性時得到了非階化Witt代數W[14].由于非階化Witt代數W本身結構更復雜，，使得對它的結構和表示的研究比Witt代數更為困難.本文生要研究無限維非階化Witt代數W系數在張量模Fα',a,b中的一階上同調群.在同構意義下，我們得到了如下的結果:其中線性映射D1,D2,D3定義如下：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 偽 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涓嬬殑緇撴灉:鍏朵腑綰挎

本文編號：1834490