Nakayama automorphisms of graded double Ore extensions of Koszul Artin-Schelter regular algebras with nontrivial skew derivations
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915401562062848 |
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| author | Cao, Yan Shen, Yuan Wang, Xin |
| author_facet | Cao, Yan Shen, Yuan Wang, Xin |
| contents | Let $A$ be a Koszul Artin-Schelter regular algebra and $B=A_P[y_1,y_2;ς,ν]$ be a graded double Ore extension of $A$ where $ς:A\to M_{2\times 2}(A)$ is a graded algebra homomorphism and $ν:A\to A^{\oplus 2}$ is a degree one $ς$-derivation. We construct a minimal free resolution for the trivial module of $B$, and it implies that $B$ is still Koszul. We introduce a homological invariant called $ς$-divergence of $ν$, and with its aid, we obtain a precise description of the Nakayama automorphism of $B$. A twisted superpotential $\hatω$ for $B$ with respect to the Nakayama automorphism is constructed so that $B$ is isomorphic to the derivation quotient algebra of $\hatω$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_15252 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nakayama automorphisms of graded double Ore extensions of Koszul Artin-Schelter regular algebras with nontrivial skew derivations Cao, Yan Shen, Yuan Wang, Xin Rings and Algebras Let $A$ be a Koszul Artin-Schelter regular algebra and $B=A_P[y_1,y_2;ς,ν]$ be a graded double Ore extension of $A$ where $ς:A\to M_{2\times 2}(A)$ is a graded algebra homomorphism and $ν:A\to A^{\oplus 2}$ is a degree one $ς$-derivation. We construct a minimal free resolution for the trivial module of $B$, and it implies that $B$ is still Koszul. We introduce a homological invariant called $ς$-divergence of $ν$, and with its aid, we obtain a precise description of the Nakayama automorphism of $B$. A twisted superpotential $\hatω$ for $B$ with respect to the Nakayama automorphism is constructed so that $B$ is isomorphic to the derivation quotient algebra of $\hatω$. |
| title | Nakayama automorphisms of graded double Ore extensions of Koszul Artin-Schelter regular algebras with nontrivial skew derivations |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2507.15252 |