From the homotopy category of projective modules over gentle algebras to poset representations
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909457593663488 |
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| author | Benitez, Germán Costa, Gustavo |
| author_facet | Benitez, Germán Costa, Gustavo |
| contents | In [BCP24], the authors describe a triangulated structure of a quotient of a certain category of representations of posets, nowadays known as the Bondarenko's category. This category was essential in [BM03] for classify all indecomposable objects of the derived category of gentle algebras. In view of this connection with the derived category, which possess a triangulated structure. In this paper, we identify another triangulated structure for Bondarenko's category, allowing us to utilize the functor presented in [BM03]. This functor will establishes a connection between the triangulated structure of the homotopy category of gentle algebras and the new triangulated structure of a quotient of a certain Bondarenko's category. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_09179 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From the homotopy category of projective modules over gentle algebras to poset representations Benitez, Germán Costa, Gustavo Representation Theory 16G20, 16G60, 16E35, 18E30 In [BCP24], the authors describe a triangulated structure of a quotient of a certain category of representations of posets, nowadays known as the Bondarenko's category. This category was essential in [BM03] for classify all indecomposable objects of the derived category of gentle algebras. In view of this connection with the derived category, which possess a triangulated structure. In this paper, we identify another triangulated structure for Bondarenko's category, allowing us to utilize the functor presented in [BM03]. This functor will establishes a connection between the triangulated structure of the homotopy category of gentle algebras and the new triangulated structure of a quotient of a certain Bondarenko's category. |
| title | From the homotopy category of projective modules over gentle algebras to poset representations |
| topic | Representation Theory 16G20, 16G60, 16E35, 18E30 |
| url | https://arxiv.org/abs/2501.09179 |