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http://hdl.handle.net/1942/32601
Title: | A categorical framework for glider representations | Authors: | HENRARD, Ruben VAN ROOSMALEN, Adam-Christiaan |
Issue Date: | 2020 | Abstract: | 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 $\Gamma$-filtered ring $FR$ and a subset $\Lambda \subseteq \Gamma$, we provide a category $\operatorname{Glid}_\Lambda FR$ 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 $\operatorname{Glid}_\Lambda FR$ 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 $\operatorname{Glid}_\Lambda FR.$ When applied to a group algebra $kG$, this shows that the monoidal category $\operatorname{Glid}_\Lambda F(kG)$ alone is sufficient to distinguish even isocategorical groups. | Keywords: | Mathematics - Representation Theory;16W70, 18E10, 18E35 | Document URI: | http://hdl.handle.net/1942/32601 | Link to publication/dataset: | http://arxiv.org/abs/2003.05930v1 | Category: | O | Type: | Preprint |
Appears in Collections: | Research publications |
Files in This Item:
File | Description | Size | Format | |
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2003.05930v1.pdf | Non Peer-reviewed author version | 565.79 kB | Adobe PDF | View/Open |
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