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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.03243 |
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| _version_ | 1866911180459606016 |
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| author | Wang, Li Wei, Jiaqun |
| author_facet | Wang, Li Wei, Jiaqun |
| contents | Let $(\mathcal{A},Θ)$ be a length category. We introduce the notation of Gabriel-Roiter measure with respect to $Θ$ and extend Gabriel's main property to this setting. Using this measure, when $(\mathcal{A},Θ)$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_03243 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The first Brauer-Thrall conjecture for extriangulated length categories Wang, Li Wei, Jiaqun Representation Theory Let $(\mathcal{A},Θ)$ be a length category. We introduce the notation of Gabriel-Roiter measure with respect to $Θ$ and extend Gabriel's main property to this setting. Using this measure, when $(\mathcal{A},Θ)$ 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. |
| title | The first Brauer-Thrall conjecture for extriangulated length categories |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2505.03243 |