论文标题
代表理论中的数量与大小
Quantity vs. size in representation theory
论文作者
论文摘要
在本说明中，我们调查了有限维代数的表示理论的两个实例，其中某种结构的数量与这些相同结构的大小密切相关。更明确地，我们回顾了以下事实：（1）有限维代数仅在且仅当每个不可兼容的模块都是有限的二维时，只有有限的不可分解的模块有限的同构模块； （2）在有限维代数上的模块类别仅在且仅当每个扭力类别由有限维模块生成时，仅在有限的许多扭转类中。
In this note, we survey two instances in the representation theory of finite-dimensional algebras where the quantity of a type of structures is intimately related to the size of those same structures. More explicitly, we review the fact that (1) a finite-dimensional algebra admits only finitely many indecomposable modules up to isomorphism if and only if every indecomposable module is finite-dimensional; (2) the category of modules over a finite-dimensional algebra admits only finitely many torsion classes if and only if every torsion class is generated by a finite-dimensional module.
