Continuous Nakayama Representations
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866916798010490880 |
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| author | Rock, Job D. Zhu, Shijie |
| author_facet | Rock, Job D. Zhu, Shijie |
| contents | We introduce continuous analogues of Nakayama algebras. In particular, we introduce the notion of (pre-)Kupisch functions, which play a role as Kupisch series of Nakayama algebras, and view continuous Nakayama representations as a special type of representation of $\mathbb{R}$ or $\mathbb{S}^1$. We investigate equivalences and connectedness of the categories of Nakayama representations. Specifically, we prove that orientation-preserving homeomorphisms on $\mathbb{R}$ and on $\mathbb{S}^1$ induce equivalences between these categories. Connectedness is characterized by a special type of points called separation points determined by (pre-)Kupisch functions. We also construct an exact embedding from the category of finite-dimensional representations for any finite-dimensional Nakayama algebra, to a category of continuous Nakayama representaitons. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_03908 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Continuous Nakayama Representations Rock, Job D. Zhu, Shijie Representation Theory We introduce continuous analogues of Nakayama algebras. In particular, we introduce the notion of (pre-)Kupisch functions, which play a role as Kupisch series of Nakayama algebras, and view continuous Nakayama representations as a special type of representation of $\mathbb{R}$ or $\mathbb{S}^1$. We investigate equivalences and connectedness of the categories of Nakayama representations. Specifically, we prove that orientation-preserving homeomorphisms on $\mathbb{R}$ and on $\mathbb{S}^1$ induce equivalences between these categories. Connectedness is characterized by a special type of points called separation points determined by (pre-)Kupisch functions. We also construct an exact embedding from the category of finite-dimensional representations for any finite-dimensional Nakayama algebra, to a category of continuous Nakayama representaitons. |
| title | Continuous Nakayama Representations |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2207.03908 |