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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.02821 |
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| _version_ | 1866914460331933696 |
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| author | Gaddis, Jason Keeler, Dennis |
| author_facet | Gaddis, Jason Keeler, Dennis |
| contents | We present a generalization of down-up algebras, originally defined by Benkart and Roby. These quiver down-up algebras arise as quotients of the double of the extended Dynkin quiver of type A. Under a certain non-degeneracy condition, we show that quiver down-up algebras are noetherian piecewise domains, and that they are twisted Calabi--Yau. Finally, we consider the isomorphism problem for graded quiver down-up algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_02821 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quiver down-up algebras of type A Gaddis, Jason Keeler, Dennis Rings and Algebras We present a generalization of down-up algebras, originally defined by Benkart and Roby. These quiver down-up algebras arise as quotients of the double of the extended Dynkin quiver of type A. Under a certain non-degeneracy condition, we show that quiver down-up algebras are noetherian piecewise domains, and that they are twisted Calabi--Yau. Finally, we consider the isomorphism problem for graded quiver down-up algebras. |
| title | Quiver down-up algebras of type A |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2512.02821 |