论文标题
有限维代数的简单反身模块
Simple reflexive modules over finite-dimensional algebras
论文作者
论文摘要
让A为有限维代数。如果A是自注，则所有模块都是反身的。 Marczinzik最近询问，如果所有简单的模块都是反身的，那么A是否必须是自注。在这里，我们展示了一个不是自注的8维代数，但所有简单的模块都是反身的（实际上，在此示例中，简单的模块是唯一的非标记不可塑性模块，它们是反思性的）。此外，我们总体上介绍了简单反射模块的一些属性。 Marczinzik通过提供大量的代数来激发他的问题，使得同类的任何代数都不是自注明的，都具有不反射性的简单模块。但是，事实证明，这些类别中的大多数属性都具有非自注的任何代数都具有简单的模块，这些模块甚至都不是无扭力的。
Let A be a finite-dimensional algebra. If A is self-injective, then all modules are reflexive. Marczinzik recently has asked whether A has to be self-injective in case all the simple modules are reflexive. Here, we exhibit an 8-dimensional algebra which is not self-injective, but such that all simple modules are reflexive (actually, for this example, the simple modules are the only non-projective indecomposable modules which are reflexive). In addition, we present some properties of simple reflexive modules in general. Marczinzik had motivated his question by providing large classes of algebras such that any algebra in the class which is not self-injective has simple modules which are not reflexive. However, as it turns out, most of these classes have the property that any algebra in the class which is not self-injective has simple modules which are not even torsionless.
