Hall algebras associated to root categories
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866909165975240704 |
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| author | Zhang, Haicheng |
| author_facet | Zhang, Haicheng |
| contents | Let $\mathcal {A}$ be a finitary hereditary abelian category. We define a Hall algebra for the root category of $\mathcal {A}$ by applying the derived Hall numbers of the bounded derived category $D^b(\mathcal {A})$, which is proved to be isomorphic to the Drinfeld double Hall algebra of $\mathcal {A}$. In the appendix, we also define the 1-periodic derived Hall algebra via the derived Hall numbers of $D^b(\mathcal {A})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_12351 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Hall algebras associated to root categories Zhang, Haicheng Representation Theory Quantum Algebra Rings and Algebras Let $\mathcal {A}$ be a finitary hereditary abelian category. We define a Hall algebra for the root category of $\mathcal {A}$ by applying the derived Hall numbers of the bounded derived category $D^b(\mathcal {A})$, which is proved to be isomorphic to the Drinfeld double Hall algebra of $\mathcal {A}$. In the appendix, we also define the 1-periodic derived Hall algebra via the derived Hall numbers of $D^b(\mathcal {A})$. |
| title | Hall algebras associated to root categories |
| topic | Representation Theory Quantum Algebra Rings and Algebras |
| url | https://arxiv.org/abs/2210.12351 |