论文标题
在特定类别的对称特殊双层代数的弦弦复合物的Auslander-Reiten组件上
On Auslander-Reiten components of string complexes for a certain class of symmetric special biserial algebras
论文作者
论文摘要
令$ \ mathbf {k} $为代数关闭字段。在本文中，我们受到V. Bekkert和H. A. Merklen获得的温和代数的派生类别中不可混合对象的描述的启发，我们为某个类$ \ Mathscr {c} $ symmetric特殊双层代数的某个类别的classcr {c} $定义了字符串复合体，这些代数是不可能的，这些代数是不可或缺的相对复杂的类别。我们还证明，如果$λ$是$ \ mathbf {k} $ - 类$ \ mathscr {c} $和$ p^\ bullet $的代数，则是$λ$的弦复合物，然后$ p^\ bullet $在其Auslander-Reiten-Reiten-Reiten-Reiten-Reiten Componep中。
Let $\mathbf{k}$ be an algebraically closed field. In this article, inspired by the description of indecomposable objects in the derived category of a gentle algebra obtained by V. Bekkert and H. A. Merklen, we define string complexes for a certain class $\mathscr{C}$ of symmetric special biserial algebras, which are indecomposable perfect complexes in the corresponding derived category. We also prove that if $Λ$ is a $\mathbf{k}$-algebra in the class $\mathscr{C}$ and $P^\bullet$ is a string complex over $Λ$, then $P^\bullet$ lies in the rim of its Auslander-Reiten component.
