论文标题
关于谎言代数同种学的注释
A note on Lie algebra cohomology
论文作者
论文摘要
鉴于有限的尺寸谎言代数$ l $让$ i $是通用封络代数$ u（l）$的增强理想。我们研究了$ l $的条件，根据该条件，当在所有$ u（l）$ - 模块的类别或$ i $ i $ -torsion $ u（l）$ u（l）$ - 模块的类别中计算时，$ ext $ groups $ ext（k，k）$（k，k）$（k，k）$是相同的。我们还证明Rees代数$ \ oplus _ {n \ geq 0} i^n $在且仅当$ l $是nilpotent时才是noetherian。给出了对肩she骨的同种学的应用。
Given a finite dimensional Lie algebra $L$ let $I$ be the augmentation ideal in the universal enveloping algebra $U(L)$. We study the conditions on $L$ under which the $Ext$-groups $Ext (k,k)$ for the trivial $L$-module $k$ are the same when computed in the category of all $U(L)$-modules or in the category of $I$-torsion $U(L)$-modules. We also prove that the Rees algebra $\oplus _{n\geq 0}I^n$ is Noetherian if and only if $L$ is nilpotent. An application to cohomology of equivariant sheaves is given.
