论文标题
平滑的竞争代数的差分形式
Differential forms on smooth operadic algebras
论文作者
论文摘要
经典的Hochschild-Kostant--Rosenberg（HKR）定理计算平滑交换代数的Hochschild同源性和共同体。在本文中，我们将此结果推广到其他类型的代数结构。我们的主要见解是，为其他类型的代数产生HKR同构与在Operad上左左模块类别中计算无准分辨率直接相关。我们确定，一旦该分辨率在对角线上，就会遵循HKR型结果。 作为示例，我们分别获得了平滑交换和光滑的支架代数的置换式和前HKR定理。我们还证明了从过滤的分布定律获得的操作的HKR定理，该定律尤其是恢复经典HKR定理的所有方面。最后，我们证明该属性是V. Dotsenko和第二作者（1804.06485）定义的Operadic PBW属性双重二元。
The classical Hochschild--Kostant--Rosenberg (HKR) theorem computes the Hochschild homology and cohomology of smooth commutative algebras. In this paper, we generalise this result to other kinds of algebraic structures. Our main insight is that producing HKR isomorphisms for other types of algebras is directly related to computing quasi-free resolutions in the category of left modules over an operad; we establish that an HKR-type result follows as soon as this resolution is diagonally pure. As examples we obtain a permutative and a pre-Lie HKR theorem for smooth commutative and smooth brace algebras, respectively. We also prove an HKR theorem for operads obtained from a filtered distributive law, which recovers, in particular, all the aspects of the classical HKR theorem. Finally, we show that this property is Koszul dual to the operadic PBW property defined by V. Dotsenko and the second author (1804.06485).
