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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2303.01670 |
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| _version_ | 1866913187364864000 |
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| author | Chen, Jiayi Lu, Ming Ruan, Shiquan |
| author_facet | Chen, Jiayi Lu, Ming Ruan, Shiquan |
| contents | For a finitary hereditary abelian category $\mathcal{A}$, we define a derived Hall algebra of its root category by counting the triangles and using the octahedral axiom, which is proved to be isomorphic to the Drinfeld double of Hall algebra of $\mathcal{A}$. When applied to finite-dimensional nilpotent representations of the Jordan quiver or coherent sheaves over elliptic curves, these algebras provide categorical realizations of the ring of Laurent symmetric functions and also double affine Hecke algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_01670 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Derived Hall algebras of root categories Chen, Jiayi Lu, Ming Ruan, Shiquan Representation Theory For a finitary hereditary abelian category $\mathcal{A}$, we define a derived Hall algebra of its root category by counting the triangles and using the octahedral axiom, which is proved to be isomorphic to the Drinfeld double of Hall algebra of $\mathcal{A}$. When applied to finite-dimensional nilpotent representations of the Jordan quiver or coherent sheaves over elliptic curves, these algebras provide categorical realizations of the ring of Laurent symmetric functions and also double affine Hecke algebras. |
| title | Derived Hall algebras of root categories |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2303.01670 |