论文标题
三个与前代数相关的Schur函数
Three Schur functors related to pre-Lie algebras
论文作者
论文摘要
我们给出了在lie代数理论中产生的三个Schur函子的明确组合描述。他们中的第一个导致对给定的谎言代数的普遍包围前代数的基础矢量空间的功能描述，从而加强了西格尔的PBW定理。另外两个Schur函子提供了通用乘法代数的基础矢量空间和给定的前代代数的Kähler差异模块的函数描述。这种描述的一个重要结果是解释了在通用乘法包裹的代数上，模块中具有系数为模块类别的派生函数的同位代数的共同体。
We give explicit combinatorial descriptions of three Schur functors arising in the theory of pre-Lie algebras. The first of them leads to a functorial description of the underlying vector space of the universal enveloping pre-Lie algebra of a given Lie algebra, strengthening the PBW theorem of Segal. The two other Schur functors provide functorial descriptions of the underlying vector spaces of the universal multiplicative enveloping algebra and of the module of Kähler differentials of a given pre-Lie algebra. An important consequence of such descriptions is an interpretation of the cohomology of a pre-Lie algebra with coefficients in a module as a derived functor for the category of modules over the universal multiplicative enveloping algebra.
