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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/2505.19921 |
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| _version_ | 1866910968721702912 |
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| author | Berger, Roland Maillard, Jun |
| author_facet | Berger, Roland Maillard, Jun |
| contents | A Poincaré Van den Bergh duality theorem for strong Kc-Calabi-Yau algebras was obtained by R. Taillefer and the first author under the assumption that the derived functors of functors involved in the statement exist. We prove the existence of these derived functors by showing that the dg category defining the derived Koszul calculus is isomorphic to a dg category of dg modules over a dg algebra. Therefore we get a definition of strong Kc-Calabi-Yau algebras and a corresponding duality theorem without any existence assumption. We prove that a polynomial algebra is strong Kc-Calabi-Yau. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_19921 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Calabi-Yau property in derived Koszul calculus Berger, Roland Maillard, Jun Representation Theory A Poincaré Van den Bergh duality theorem for strong Kc-Calabi-Yau algebras was obtained by R. Taillefer and the first author under the assumption that the derived functors of functors involved in the statement exist. We prove the existence of these derived functors by showing that the dg category defining the derived Koszul calculus is isomorphic to a dg category of dg modules over a dg algebra. Therefore we get a definition of strong Kc-Calabi-Yau algebras and a corresponding duality theorem without any existence assumption. We prove that a polynomial algebra is strong Kc-Calabi-Yau. |
| title | Calabi-Yau property in derived Koszul calculus |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2505.19921 |