论文标题
连续的中山表示
Continuous Nakayama Representations
论文作者
论文摘要
我们介绍了Nakayama代数的连续类比。特别是，我们介绍了（Pre-）kupisch函数的概念，这些函数扮演着库皮斯（Kupisch）系列中的nakayama代数，并将连续的nakayama表示形式视为$ \ mathbb {r} $或$ \ mathbb {s} s}^1 $的特殊类型。我们调查了Nakayama表示类别的等价和联系。具体来说，我们证明了$ \ mathbb {r} $以及$ \ mathbb {s}^1 $在这些类别之间引起等价的$ \ mathbb {r} $上的定向性同态。连接性的特征是特殊类型的点，称为分离点，由（Pre-）kupisch函数确定。我们还为任何有限维nakayama代数的有限维表示类别构建了一个确切的嵌入，以构建到连续的nakayama代表代表。
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.
