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arXiv · 2505.03243

The first Brauer-Thrall conjecture for extriangulated length categories

Li Wang·Jiaqun Wei
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Abstract

Let $(\mathcal{A},\Theta)$ be a length category. We introduce the notation of Gabriel-Roiter measure with respect to $\Theta$ and extend Gabriel's main property to this setting. Using this measure, when $(\mathcal{A},\Theta)$ satisfies some technical conditions, we prove that $\mathcal{A}$ has an infinite number of pairwise nonisomorphic indecomposable objects if and only if it has indecomposable objects of arbitrarily large length. That is, the first Brauer-Thrall conjecture holds.

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BibTeXRIS

Li Wang, Jiaqun Wei. 2025-05-06. The first Brauer-Thrall conjecture for extriangulated length categories. https://arxiv.org/abs/2505.03243

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