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arXiv · 1408.6452

On components of stable Auslander-Reiten quivers that contain Heller lattices: the case of truncated polynomial rings

Susumu Ariki·Ryoichi Kase·Kengo Miyamoto
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Abstract

Let $A$ be a truncated polynomial ring over a complete discrete valuation ring $\mathcal{O}$, and we consider the additive category consisting of $A$-lattices $M$ with the property that $M\otimes \mathcal{K}$ is projective as an $A\otimes \mathcal{K}$-module, where $\mathcal{K}$ is the fraction field of $\mathcal{O}$. Then, we may define the stable Auslander-Reiten quiver of the category. We determine the shape of the components of the stable Auslander-Reiten quiver that contain Heller lattices.

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Susumu Ariki, Ryoichi Kase, Kengo Miyamoto. 2014-08-27. On components of stable Auslander-Reiten quivers that contain Heller lattices: the case of truncated polynomial rings. https://arxiv.org/abs/1408.6452

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