Virasoro type Lie algebras and deformations
Virasoro type Lie algebras and deformations
复制标题
DOI：
10.1007/s002880050272
复制
发表时间：
1996
期刊：
影响因子：
--
通讯作者：
A. Dzhumadil'daev
中科院分区：
文献类型：
--
作者：
A. Dzhumadil'daev
计算了系数为不可约张量模的Cartan型李代数的第一和第二上同调。spaceH1（L， U）被解释为（L， U）-模块的变形空间。H2(L， L)≠0 ifL=S2,S2+orL=Hn,Hn+。无散度向量场的李代数只有一个非平凡的局部变形。双侧简单哈密顿代数除Moyal循环外，还增加了2n2+n个新的局部变形。李代数l =Wn(n>3),Sn−1(n>2),Hn(n>1),Kn+1（n>1）具有3,1,1,3个具有不可约基和非零1-上同调的非同构张量模；2-上同列对应的数分别为9、6、7和9。
The first and second cohomologies of Cartan Type Lie algebras with coefficients in irreducible tensor modules are calculated. The spaceH1(L, U) is interpreted as a space of deformations of (L, U)-modules.H2(L, L)≠0 ifL=S2,S2+orL=Hn,Hn+. Lie algebra of divergenceless vector fieldsS2+has only one nontrivial local deformation. The two-sided simple hamiltonian algebraHnhas 2n2+nnew local deformations in addition to Moyal cocycle. The Lie algebrasL=Wn(n>3),Sn−1(n>2),Hn(n>1),Kn+1(n>1) have 3, 1, 1, 3 nonisomorphic tensor modules with irreducible bases and nonzero 1-cohomologies; respectively, the corresponding numbers for 2-cohomologies are 9, 6, 7 and 9.