论文标题
Koszul微积分中的杯帽二元性
A cup-cap duality in Koszul calculus
论文作者
论文摘要
我们在N均质代数的Koszul计算中引入了杯帽双重性。作为一种应用，我们证明了Koszul Cap产品的分级对称性是Koszul Cup产品的分级通勤性的结果。我们提出了一种概念性方法，该方法可能会导致基于DG代数和DG Bimodules框架中的派生类别的分级交换性证明。在较弱的情况下，开发了各种富集的结构，与N> 2相对应。
We introduce a cup-cap duality in the Koszul calculus of N-homogeneous algebras. As an application, we prove that the graded symmetry of the Koszul cap product is a consequence of the graded commutativity of the Koszul cup product. We propose a conceptual approach that may lead to a proof of the graded commutativity, based on derived categories in the framework of DG algebras and DG bimodules. Various enriched structures are developed in a weaker situation corresponding to N>2.
