论文标题
关于矢量场亚代代代代代代代代数的有限维度
On finite dimensionality of homology of subalgebras of vector fields
论文作者
论文摘要
我们表明，张量字段模块的张量产品是一个Noetherian模块，作为在$ \ Mathbb {r}^n $上的多项式矢量字段的Lie代数中的任何有限层代数中的任何分级的子代数的模块。 作为推论，我们证明了I.M.Gelfand的猜想在ICM'1970宣布，尼斯（NICE）上的有限维度有限的级别共同体学的有限层，正式矢量字段的like lie子代理$ w_n $。
We show that the tensor product of modules of tensor fields is a noetherian module as a module over any graded Lie subalgebra of finite codimension in the Lie algebra of polynomial vector fields on $\mathbb{R}^n$. As a corollary, we prove the conjecture of I.M.Gelfand announced at ICM'1970 at Nice on finite dimensionality of continuous cohomology of graded Lie subalgebras of formal vector fields $W_n$.
