Simple transitive 2-representations of bimodules over radical square zero Nakayama algebras via localization
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866914924514508800 |
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| author | Jonsson, Helena Stroiński, Mateusz |
| author_facet | Jonsson, Helena Stroiński, Mateusz |
| contents | We study the classification problem of simple transitive 2-representations of the 2-category of finite-dimensional bimodules over a radical square zero Nakayama algebra. This results in a complete classification of simple transitive 2-representations whose apex is a finitary two-sided cell. We define a notion of localization of 2-representations. We construct previously unknown simple transitive 2-representations as localizations of cell 2-representations. Using the universal property of our construction we prove that any simple transitive 2-representation with finitary apex is equivalent to a localization of a cell 2-representation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_09590 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Simple transitive 2-representations of bimodules over radical square zero Nakayama algebras via localization Jonsson, Helena Stroiński, Mateusz Representation Theory 18N10, 16D20, 16G10 We study the classification problem of simple transitive 2-representations of the 2-category of finite-dimensional bimodules over a radical square zero Nakayama algebra. This results in a complete classification of simple transitive 2-representations whose apex is a finitary two-sided cell. We define a notion of localization of 2-representations. We construct previously unknown simple transitive 2-representations as localizations of cell 2-representations. Using the universal property of our construction we prove that any simple transitive 2-representation with finitary apex is equivalent to a localization of a cell 2-representation. |
| title | Simple transitive 2-representations of bimodules over radical square zero Nakayama algebras via localization |
| topic | Representation Theory 18N10, 16D20, 16G10 |
| url | https://arxiv.org/abs/2112.09590 |