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arXiv · 2604.20649

Trivial extensions of Koszul Artin-Schelter regular algebras

Kenta Ueyama
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Abstract

Let $S$ be an $\mathbb N$-graded Koszul Artin-Schelter regular algebra and let $\sigma$ be a graded algebra automorphism of $S$. We study the stable category of graded maximal Cohen-Macaulay modules over the trivial extension algebra $S\ltimes S_\sigma(-1)$. 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 $S^{\sigma^{-1}}$. 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.

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Kenta Ueyama. 2026-04-22. Trivial extensions of Koszul Artin-Schelter regular algebras. https://arxiv.org/abs/2604.20649

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