论文标题
$ \ text {Assder} $ Pairs的扩展，变形和分类
Extensions, deformation and categorification of $\text{AssDer}$ pairs
论文作者
论文摘要
在本文中，我们考虑配备有推导的联想代数。这样的一对具有派生的关联代数称为Assder对。使用Hochschild共同体来进行联想代数，我们定义了一个具有代表系数的Assder对。我们研究中央延伸和阿贝尔的分析。此外，我们考虑了在联想代数的中央扩展中的一对推导物的扩展。接下来，我们通过将关联产物和推导物变形来研究Assder对的形式的单参数变形。它们由Assder对的同时理论与代表本身管理。在下一部分中，我们研究了$ 2 $ -Term $ a_ \ infty $ - 代数，其中包括Loday和Doubek-Lada考虑的同型派生。最后，我们引入了$ 2 $衍生的$ 2 $ - 代数，并表明$ 2 $衍生的$ 2 $ algebras类别等于$ 2 $ -Term $ a_ \ a_ \ a_ \ in_ \ infty $ - infty $ - 代数，并带有同质衍生物。
In this paper, we consider associative algebras equipped with derivations. Such a pair of an associative algebra with a derivation is called an AssDer pair. Using the Hochschild cohomology for associative algebras, we define cohomology for an AssDer pair with coefficients in a representation. We study central extensions and abelian extensions of AssDer pairs. Moreover, we consider extensions of a pair of derivations in central extensions of associative algebras. Next, we study formal one-parameter deformations of AssDer pair by deforming both the associative product and the derivation. They are governed by the cohomology of the AssDer pair with representation in itself. In the next part, we study $2$-term $A_\infty$-algebras with homotopy derivations considered by Loday and Doubek-Lada. Finally, we introduce $2$-derivations on associative $2$-algebras and show that the category of associative $2$-algebras with $2$-derivations are equivalent to the category of $2$-term $A_\infty$-algebras with homotopy derivations.
