论文标题
滑翔机表示的分类框架
A categorical framework for glider representations
论文作者
论文摘要
片段和滑翔机表示（由F. Caenepeel，S。Nawal和F. van Oystaeyen引入）形成了过滤模块上过滤环上的概括。给定$γ$滤清的环$ fr $和子集$λ\子群γ$，我们提供了Glider表示的类别$ \ permatatorName {glid}_λfr$，并表明它是一个完整且完整的质量质量质量质量。我们讨论其派生类别及其自然滑翔机和Noether Gliders的子类别。 如果$ r $是field $ k $的bialgebra，而$ fr $是bialgebras的过滤，我们表明$ \ operatotorname {glid}_λfr$是一个单型类别，是一个单型类别，它是等效于半hopf类别类别的类别的类别（在e.batista，s. caenepeel，seenepeel和s. caenepeel的含义上，以及J. veruy e. veruy。我们表明，与一步过滤相关的滑翔机表示的单类别类别$ k \ cdot 1 \ subseteq r $ a bialgebra $ r $的subseteq r $足以通过从$ \ operatorname {glid}_λfr。 $ \ operatatorName {glid}_λf（kg）$仅足以区分等分类组。
Fragment and glider representations (introduced by F. Caenepeel, S. Nawal, and F. Van Oystaeyen) form a generalization of filtered modules over a filtered ring. Given a $Γ$-filtered ring $FR$ and a subset $Λ\subseteq Γ$, we provide a category $\operatorname{Glid}_ΛFR$ of glider representations, and show that it is a complete and cocomplete deflation quasi-abelian category. We discuss its derived category, and its subcategories of natural gliders and Noetherian gliders. If $R$ is a bialgebra over a field $k$ and $FR$ is a filtration by bialgebras, we show that $\operatorname{Glid}_ΛFR$ is a monoidal category which is derived equivalent to the category of representations of a semi-Hopf category (in the sense of E. Batista, S. Caenepeel, and J. Vercruysse). We show that the monoidal category of glider representations associated to the one-step filtration $k \cdot 1 \subseteq R$ of a bialgebra $R$ is sufficient to recover the bialgebra $R$ by recovering the usual fiber functor from $\operatorname{Glid}_ΛFR.$ When applied to a group algebra $kG$, this shows that the monoidal category $\operatorname{Glid}_ΛF(kG)$ alone is sufficient to distinguish even isocategorical groups.
