论文标题
Chevalley-Eilenberg函子上的混合分级结构
Mixed graded structure on Chevalley-Eilenberg functors
论文作者
论文摘要
在本文中，我们将提供纯粹的$ \ infty $ - 分类结构，该分类结构是Chevalley-eilenberg Complexsing Compucting Compucting Compucting Computing Computing Compure and Cologology和Lie代数的共同体，这些代数定义在特征的特征性$ 0 $ 0上。虽然预计Chevalley-Eilenberg Complexs上的这种额外的结构是可以预期的，并且已经用链复合物给出的明确模型进行了描述，但在可用文献中，没有完全正式和模型的独立描述。在构建所有细节之后，Chevalley-Eilenberg $ \ infty $ functors并研究其主要正式属性，我们就其行为提出了一些进一步的猜想。
In this paper, we shall provide a purely $\infty$-categorical construction of the mixed graded structure over Chevalley-Eilenberg complexes computing homology and cohomology of Lie algebras defined over a field $\Bbbk$ of characteristic $0$. While this additional piece of structure on Chevalley-Eilenberg complexes is expected, and already described in terms of explicit models given by chain complexes, there is not a completely formal and model independent description of the mixed graded Chevalley-Eilenberg $\infty$-functors in available literature. After constructing in all details the Chevalley-Eilenberg $\infty$-functors and studying their main formal properties, we present some further conjectures on their behavior.
