发表机构
Institut Camille Jordan, Université de Lyon 1; Section de Mathématiques, Université de Genève（里昂第一大学卡米尔·若尔当研究所; 日内瓦大学数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文定义了余交换Hopf代数上模的广泛可均性，证明了其与可均性及短正合列的关系，并讨论了置换模与外代数情形。
AI 中文摘要
对于余交换Hopf代数\\(\mathscr A\\)上的模\\(M\\)，我们通过其对称代数作为\\(\operatorname{Sym}(M)\\#\mathscr A\\)上的模的可均性来定义广泛可均性。利用作者的余代数舍入和商定理，我们证明了非零广泛可均模是可均的，每个可均Hopf代数上的模都是广泛可均的，并且广泛可均性由短正合列保持和反映。对于置换模，此定义在任意域上与群作用的广泛可均性一致。最后一节给出了外代数的修改，并在若干情形下建立了两种定义之间的比较。
英文摘要
For a module \(M\) over a cocommutative Hopf algebra \(\mathscr A\), we define extensive amenability by amenability of its symmetric algebra as a module over \(\operatorname{Sym}(M)\#\mathscr A\). Using the author's coalgebraic rounding and quotient theorems, we prove that nonzero extensively amenable modules are amenable, that every module over an amenable Hopf algebra is extensively amenable, and that extensive amenability is preserved and reflected by short exact sequences. For permutation modules this definition agrees, over every field, with extensive amenability of group actions. A final section gives the modifications for exterior algebras and establishes the comparison between the two definitions in several cases.
CommentsSome parts of the text were written with the help of ChatGPT Astra
