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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.18604 |
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| _version_ | 1866909362651398144 |
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| author | Contu, Alessandro |
| author_facet | Contu, Alessandro |
| contents | Using Hernandez-Leclerc's isomorphism between the derived Hall algebra of a representation-finite quiver $Q$ and the quantum Grothendieck ring of the quantum loop algebra of the Dynkin type of $Q$, we lift the (quantum) cluster algebra structure of the quantum Grothendieck ring to the semi-derived Hall algebra, introduced by Gorsky, of the category of bounded complexes of projective modules over the path algebra of $Q$. We also construct a braid group action on the semi-derived Hall algebra, lifting Kashiwara-Kim-Oh-Park's braid group action on the quantum Grothendieck ring. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_18604 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A quantum cluster algebra structure on the semi-derived Hall algebra Contu, Alessandro Representation Theory 13F60 (Primary) 17B37, 18G80 (Secondary) Using Hernandez-Leclerc's isomorphism between the derived Hall algebra of a representation-finite quiver $Q$ and the quantum Grothendieck ring of the quantum loop algebra of the Dynkin type of $Q$, we lift the (quantum) cluster algebra structure of the quantum Grothendieck ring to the semi-derived Hall algebra, introduced by Gorsky, of the category of bounded complexes of projective modules over the path algebra of $Q$. We also construct a braid group action on the semi-derived Hall algebra, lifting Kashiwara-Kim-Oh-Park's braid group action on the quantum Grothendieck ring. |
| title | A quantum cluster algebra structure on the semi-derived Hall algebra |
| topic | Representation Theory 13F60 (Primary) 17B37, 18G80 (Secondary) |
| url | https://arxiv.org/abs/2410.18604 |