A Note on Odd Periodic derived Hall algebras
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911850073948160 |
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| author | Zhang, Haicheng Zhang, Xinran Zhu, Zhiwei |
| author_facet | Zhang, Haicheng Zhang, Xinran Zhu, Zhiwei |
| contents | Let $m$ be an odd positive integer and $D_m(\mathcal {A})$ be the $m$-periodic derived category of a finitary hereditary abelian category $\mathcal {A}$. In this note, we prove that there is an embedding of algebras from the derived Hall algebra of $D_m(\mathcal {A})$ defined by Xu-Chen [13] to the extended derived Hall algebra of $D_m(\mathcal {A})$ defined in [16]. This homomorphism is given on basis elements, rather than just on generating elements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_09071 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Note on Odd Periodic derived Hall algebras Zhang, Haicheng Zhang, Xinran Zhu, Zhiwei Representation Theory Quantum Algebra Rings and Algebras Let $m$ be an odd positive integer and $D_m(\mathcal {A})$ be the $m$-periodic derived category of a finitary hereditary abelian category $\mathcal {A}$. In this note, we prove that there is an embedding of algebras from the derived Hall algebra of $D_m(\mathcal {A})$ defined by Xu-Chen [13] to the extended derived Hall algebra of $D_m(\mathcal {A})$ defined in [16]. This homomorphism is given on basis elements, rather than just on generating elements. |
| title | A Note on Odd Periodic derived Hall algebras |
| topic | Representation Theory Quantum Algebra Rings and Algebras |
| url | https://arxiv.org/abs/2307.09071 |