The Grothendieck group of a triangulated category
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916340332232704 |
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| author | Chen, Xiao-Wu Li, Zhi-Wei Zhang, Xiaojin Zhao, Zhibing |
| author_facet | Chen, Xiao-Wu Li, Zhi-Wei Zhang, Xiaojin Zhao, Zhibing |
| contents | We give a direct proof of the following known result: the Grothendieck group of a triangulated category with a silting subcategory is isomorphic to the split Grothendieck group of the silting subcategory. Moreover, we obtain its cluster-tilting analogue. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_15800 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Grothendieck group of a triangulated category Chen, Xiao-Wu Li, Zhi-Wei Zhang, Xiaojin Zhao, Zhibing Representation Theory Category Theory 18G80, 18F30 We give a direct proof of the following known result: the Grothendieck group of a triangulated category with a silting subcategory is isomorphic to the split Grothendieck group of the silting subcategory. Moreover, we obtain its cluster-tilting analogue. |
| title | The Grothendieck group of a triangulated category |
| topic | Representation Theory Category Theory 18G80, 18F30 |
| url | https://arxiv.org/abs/2404.15800 |