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 a continuous Nakayama representation 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.

我们引入中山代数的连续类似物。特别是，我们引入了（前）Kupisch 函数的概念，它充当 Nakayama 代数的 Kupisch 级数，并将连续 Nakayama 表示视为 \({\mathbb {R}}\) 的特殊类型表示或\({\mathbb {S}}^1\)。我们研究中山表示类别的等价性和连通性。具体来说，我们证明了\({\mathbb {R}}\)和\({\mathbb {S}}^1\)上的方向保持同态归纳这些类别之间的等价性。连通性的特征是一种特殊类型的点，称为分离点，由（前）库皮施函数确定。我们还构建了从任何有限维 Nakayama 代数的有限维表示类别到连续 Nakayama 表示类别的精确嵌入。