发表机构
Department of Mathematics, UFSCar, Brazil（联邦圣卡洛斯大学数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文分类了分裂群代数上的分次双模，通过双陪集、稳定子特征和系数模给出分类，并计算Peirce分量，否定回答了非交换情形下的一个开放问题。
AI 中文摘要
我们分类了任意群中有限阿贝尔子群的分裂群代数上的分次双模，分类结果由双陪集、稳定子特征和系数模刻画。在域上，我们确定了Yetter-Drinfel'd模的诱导函子的本质像，对Dos Santos和Yasumura在非交换情形下的问题给出了否定回答。我们还计算了Peirce分量，并通过稳定子特征的扩张刻画了无重数双模。
英文摘要
We classify, up to graded isomorphism, graded bimodules over split group algebras of finite abelian subgroups of an arbitrary group. The classification is governed by double cosets, stabilizer characters, and coefficient modules. Over a field, we determine the essential image of the induction functor on Yetter-Drinfel'd modules, giving a negative answer to a question of Dos Santos and Yasumura in the nonabelian case. We also compute the Peirce components and characterize multiplicity-free bimodules through extensions of stabilizer characters.
Comments20 pages
