Continuous quivers of type A (I) Foundations
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2019
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| Acceso en línea: | |
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| _version_ | 1866912436961935360 |
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| author | Igusa, Kiyoshi Rock, Job D. Todorov, Gordana |
| author_facet | Igusa, Kiyoshi Rock, Job D. Todorov, Gordana |
| contents | We generalize type $A$ quivers to continuous type $A$ quivers and prove initial results about pointwise finite-dimensional (pwf) representations. We classify the indecomosable pwf representations and provide a decomposition theorem, recovering results of Botnan and Crawley-Boevey. We also classify the indecomposable pwf projective representations. Finally, we prove that many of the properties of finite-dimensional type $A_n$ representations are present in finitely generated pwf representations. This is the self-contained foundational part of a series of works to study a generalization of continuous clusters categories and their relationship to other type $A$ cluster structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1909_10499 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Continuous quivers of type A (I) Foundations Igusa, Kiyoshi Rock, Job D. Todorov, Gordana Representation Theory 18E30: 16G20 We generalize type $A$ quivers to continuous type $A$ quivers and prove initial results about pointwise finite-dimensional (pwf) representations. We classify the indecomosable pwf representations and provide a decomposition theorem, recovering results of Botnan and Crawley-Boevey. We also classify the indecomposable pwf projective representations. Finally, we prove that many of the properties of finite-dimensional type $A_n$ representations are present in finitely generated pwf representations. This is the self-contained foundational part of a series of works to study a generalization of continuous clusters categories and their relationship to other type $A$ cluster structures. |
| title | Continuous quivers of type A (I) Foundations |
| topic | Representation Theory 18E30: 16G20 |
| url | https://arxiv.org/abs/1909.10499 |