Finite Dimensional Representations of Quivers with Oriented Cycles
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916527037480960 |
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| author | Goodearl, K. R. Huisgen-Zimmermann, B. |
| author_facet | Goodearl, K. R. Huisgen-Zimmermann, B. |
| contents | Let $K$ be a field, $Q$ a quiver, and $\mathcal{A}$ the ideal of the path algebra $KQ$ that is generated by the arrows of $Q$. We present old and new results about the representation theories of the truncations $KQ/\mathcal{A}^L$, $L \in \mathbb{N}$, tracking their development as $L$ goes to infinity. The goal is to gain a better understanding of the category of those finite dimensional $KQ$-modules which arise as finitely generated modules over admissible quotients of $KQ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_12431 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Finite Dimensional Representations of Quivers with Oriented Cycles Goodearl, K. R. Huisgen-Zimmermann, B. Representation Theory Rings and Algebras 16D70, 16D90, 16G20, 16P10 Let $K$ be a field, $Q$ a quiver, and $\mathcal{A}$ the ideal of the path algebra $KQ$ that is generated by the arrows of $Q$. We present old and new results about the representation theories of the truncations $KQ/\mathcal{A}^L$, $L \in \mathbb{N}$, tracking their development as $L$ goes to infinity. The goal is to gain a better understanding of the category of those finite dimensional $KQ$-modules which arise as finitely generated modules over admissible quotients of $KQ$. |
| title | Finite Dimensional Representations of Quivers with Oriented Cycles |
| topic | Representation Theory Rings and Algebras 16D70, 16D90, 16G20, 16P10 |
| url | https://arxiv.org/abs/2412.12431 |