Categories of generalized thread quivers
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915104956612608 |
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| author | Paquette, Charles Rock, Job Daisie Yıldırım, Emine |
| author_facet | Paquette, Charles Rock, Job Daisie Yıldırım, Emine |
| contents | We study the representation category of thread quivers and their quotients. A thread quiver is a quiver in which some arrows have been replaced by totally ordered sets. Pointwise finite-dimensional (pwf) representations of such a thread quiver admit a Krull-Remak-Schmidt-Azumaya decomposition. We show that an indecomposable representation is induced from an indecomposable representation of a quiver obtained from the original quiver by replacing some of its arrows by a finite linear $\mathbb{A}_n$ quiver. We study injective and projective pwf indecomposable representations and we fully classify them when the quiver satisfies a mild condition. We give a characterization of the indecomposable pwf representations of certain categories whose representation theory has similar properties to finite type or tame type. We further construct new hereditary abelian categories, including a Serre subcategory of pwf representations that includes every indecomposable representation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_14656 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Categories of generalized thread quivers Paquette, Charles Rock, Job Daisie Yıldırım, Emine Representation Theory 16G20 We study the representation category of thread quivers and their quotients. A thread quiver is a quiver in which some arrows have been replaced by totally ordered sets. Pointwise finite-dimensional (pwf) representations of such a thread quiver admit a Krull-Remak-Schmidt-Azumaya decomposition. We show that an indecomposable representation is induced from an indecomposable representation of a quiver obtained from the original quiver by replacing some of its arrows by a finite linear $\mathbb{A}_n$ quiver. We study injective and projective pwf indecomposable representations and we fully classify them when the quiver satisfies a mild condition. We give a characterization of the indecomposable pwf representations of certain categories whose representation theory has similar properties to finite type or tame type. We further construct new hereditary abelian categories, including a Serre subcategory of pwf representations that includes every indecomposable representation. |
| title | Categories of generalized thread quivers |
| topic | Representation Theory 16G20 |
| url | https://arxiv.org/abs/2410.14656 |