We define group-twisted Alexander-Whitney and Eilenberg-Zilber maps for converting between bimodule resolutions of skew group algebras. These algebras are the natural semidirect products recording actions of finite groups by automorphisms. The group-twisted chain maps allow us to transfer information between resolutions for use in homology theories, for example, in those governing deformation theory. We show how to translate in particular from the default (but often cumbersome) reduced bar resolution to a more convenient twisted product resolution. This provides a more universal approach to some known results classifying PBW deformations.

我们定义了群扭曲的Alexander-Whitney和Eilenberg-Zilber映射，用于在偏群代数的双模分辨率之间进行转换。这些代数是自然半直接乘积，它通过自同构记录有限组的作用。群扭链图使我们能够在分辨率之间传递信息，以用于同源理论，例如，在那些控制变形理论的理论中。我们将展示如何从默认的（但通常很麻烦）降低的条分辨率转换为更方便的扭曲产品分辨率的方法。这为对PBW变形进行分类的一些已知结果提供了更通用的方法。