标题： 变形理论与Koszul代数上的Hopf作用 显示英文标题

标题： Deformation Theory and Hopf Actions on Koszul Algebras

摘要： 我们考虑在非交换代数上定义的代数的分次变形和PBW变形。 我们解释分次变形的纤维如何对应于具有PBW性质的过滤代数，重点在于Hopf代数作用于二次代数的乘积代数。 特别是，我们描述了来自Koszul代数上的Hopf作用的所有PBW变形，给出了Hopf-Koszul Hecke代数。 扭曲张量积的Alexander-Whitney和Eilenberg-Zilber映射在分解之间传递同调信息，并将Hochschild上循环和Gerstenhaber括号的条件转化为显式的PBW条件。 显示英文摘要

摘要： We consider graded deformations and PBW deformations of algebras defined over noncommutative algebras. We explain how fibers of graded deformations correspond to filtered algebras admitting a PBW property, with focus on smash product algebras for Hopf algebras acting on quadratic algebras. In particular, we describe all PBW deformations arising from Hopf actions on Koszul algebras, giving Hopf-Koszul Hecke algebras. Alexander-Whitney and Eilenberg-Zilber maps for twisted tensor products transfer homological information between resolutions and convert conditions on Hochschild cocycles and Gerstenhaber brackets into explicit PBW conditions.