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arXiv · 2510.15252

The derived Hall algebra of a graded gentle one-cycle algebra I: the triangle structure

Hui Chen·Dong Yang
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Abstract

Under a mild condition, the perfect derived category and the finite-dimensional derived category of a graded gentle one-cycle algebra are described as twisted root categories of certain infinite quivers of type $\mathbb{A}_\infty^\infty$. As a consequence, it is shown that if $\ct$ is the perfect (respectively, finite-dimensional) derived category of such a graded gentle one-cycle algebra, then its triangle structure is up to triangle equivalence determined by the underlying additive category.

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Hui Chen, Dong Yang. 2025-10-17. The derived Hall algebra of a graded gentle one-cycle algebra I: the triangle structure. https://arxiv.org/abs/2510.15252

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