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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.05687 |
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| _version_ | 1866929405244211200 |
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| author | Ohara, Mariko |
| author_facet | Ohara, Mariko |
| contents | Let H be a finite dimensional Hopf algebra over a field k and A an H-module algebra over k. Khovanov and Qi defined acyclic objects and quasi-isomorphisms by using null-homotopy and contractible objects. They also defined the cofibrant objects, the derived category of A#H-modules, and showed properties of compact generators. On the other hand, a model structure on the category of A#H-modules are not mentioned yet. In this paper, we check that the category of A#H-modules admits a model structure, where the cofibrant objects and the derived category are just those defined by Qi. We also show that the model structure is cofibrantly generated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_05687 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A model structure on the category of equivariant A-modules over a Hopf algebra Ohara, Mariko K-Theory and Homology 16T05, 16S40, 18G65, 18G80, 20G42 Let H be a finite dimensional Hopf algebra over a field k and A an H-module algebra over k. Khovanov and Qi defined acyclic objects and quasi-isomorphisms by using null-homotopy and contractible objects. They also defined the cofibrant objects, the derived category of A#H-modules, and showed properties of compact generators. On the other hand, a model structure on the category of A#H-modules are not mentioned yet. In this paper, we check that the category of A#H-modules admits a model structure, where the cofibrant objects and the derived category are just those defined by Qi. We also show that the model structure is cofibrantly generated. |
| title | A model structure on the category of equivariant A-modules over a Hopf algebra |
| topic | K-Theory and Homology 16T05, 16S40, 18G65, 18G80, 20G42 |
| url | https://arxiv.org/abs/2401.05687 |