论文标题
弧图和2期简单的$ a $ typer代数的简单集合
Arc diagrams and 2-term simple-minded collections of preprojective algebras of type $A$
论文作者
论文摘要
我们通过ARC图研究了对$ A $类型的预定代数的半光和两项简单集合的明确描述。我们在一组非交叉弧图（分别是双弧图的集合）之间提供了两者，该图与对称组的元素相对应，而在代数上是对对称组的元素的二十字图（分别与对称组元素的元素），以及一组半光（sep。此外，我们在一组双弧图图上定义了一个突变和部分顺序。特别是，我们在对称群体和一组2项简单的集合之间获得了同构的同构。作为结果的应用，我们研究了$ a $ $ a $的前代数代数的某些商代数的半光，我们谴责了其他作者所显示的一些重要结果。
We study an explicit description of semibricks and 2-term simple-minded collections over preprojective algebras of type $A$ via arc diagrams. We provide a bijection between the set of noncrossoing arc diagrams (resp. the set of double arc diagrams), which is in bijective correspondence with elements of the symmetric group, and the set of semibricks (resp. the set of 2-term simple-minded collections) over the algebra. Moreover we define a mutation and a partial order on the set of double arc diagrams. In particular, we obtain a poset isomorphism between the symmetric group and the set of 2-term simple-minded collections. As an application of our results, we study semibricks of some quotient algebras of the preprojective algebras of type $A$ and we reprove some important results shown by the other authors.
