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http://hdl.handle.net/1942/32601
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DC Field | Value | Language |
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dc.contributor.author | HENRARD, Ruben | - |
dc.contributor.author | VAN ROOSMALEN, Adam-Christiaan | - |
dc.date.accessioned | 2020-11-12T14:20:02Z | - |
dc.date.available | 2020-11-12T14:20:02Z | - |
dc.date.issued | 2020 | - |
dc.date.submitted | 2020-11-11T14:44:46Z | - |
dc.identifier.uri | http://hdl.handle.net/1942/32601 | - |
dc.description.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. | - |
dc.language.iso | en | - |
dc.subject | Mathematics - Representation Theory | - |
dc.subject | Mathematics - Representation Theory | - |
dc.subject | 16W70, 18E10, 18E35 | - |
dc.subject.other | Mathematics - Representation Theory | - |
dc.subject.other | 16W70, 18E10, 18E35 | - |
dc.title | A categorical framework for glider representations | - |
dc.type | Preprint | - |
local.format.pages | 33 | - |
local.bibliographicCitation.jcat | O | - |
local.type.refereed | Non-Refereed | - |
local.type.specified | Preprint | - |
dc.identifier.arxiv | 2003.05930 | - |
dc.identifier.url | http://arxiv.org/abs/2003.05930v1 | - |
local.provider.type | ArXiv | - |
local.uhasselt.uhpub | yes | - |
item.fulltext | With Fulltext | - |
item.contributor | HENRARD, Ruben | - |
item.contributor | VAN ROOSMALEN, Adam-Christiaan | - |
item.accessRights | Open Access | - |
item.fullcitation | HENRARD, Ruben & VAN ROOSMALEN, Adam-Christiaan (2020) A categorical framework for glider representations. | - |
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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