Continuous Nakayama Representations
Abstrak
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.
Topik & Kata Kunci
Penulis (2)
Job D. Rock
Shijie Zhu
Akses Cepat
- Tahun Terbit
- 2022
- Bahasa
- en
- Sumber Database
- arXiv
- Akses
- Open Access ✓