Trivial extensions of Koszul Artin-Schelter regular algebras
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915949407371264 |
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| author | Ueyama, Kenta |
| author_facet | Ueyama, Kenta |
| contents | Let $S$ be an $\mathbb N$-graded Koszul Artin-Schelter regular algebra and let $σ$ be a graded algebra automorphism of $S$. We study the stable category of graded maximal Cohen-Macaulay modules over the trivial extension algebra $S\ltimes S_σ(-1)$. We show that this category is triangle equivalent to the bounded derived category of finitely generated (ungraded) modules over the Koszul dual algebra of the Zhang twist $S^{σ^{-1}}$. In the connected graded case, we also obtain a criterion for when two such stable categories are triangle equivalent, and show that such an equivalence induces an equivalence between the categories of graded modules over the original algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_20649 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Trivial extensions of Koszul Artin-Schelter regular algebras Ueyama, Kenta Rings and Algebras Representation Theory Let $S$ be an $\mathbb N$-graded Koszul Artin-Schelter regular algebra and let $σ$ be a graded algebra automorphism of $S$. We study the stable category of graded maximal Cohen-Macaulay modules over the trivial extension algebra $S\ltimes S_σ(-1)$. We show that this category is triangle equivalent to the bounded derived category of finitely generated (ungraded) modules over the Koszul dual algebra of the Zhang twist $S^{σ^{-1}}$. In the connected graded case, we also obtain a criterion for when two such stable categories are triangle equivalent, and show that such an equivalence induces an equivalence between the categories of graded modules over the original algebras. |
| title | Trivial extensions of Koszul Artin-Schelter regular algebras |
| topic | Rings and Algebras Representation Theory |
| url | https://arxiv.org/abs/2604.20649 |