论文标题
温和代数的派生类别中的特殊序列
Exceptional sequences in the derived category of a gentle algebra
论文作者
论文摘要
在本文中，使用柔和的代数和标记表面的解剖的对应关系，我们研究了柔和的代数$ \ Mathsf {a a} $的完美衍生类别中的完整典型序列$ \ mathsf {k^b（a）} $。我们表明，当且仅当关联标记的表面没有穿刺并且边界上至少有两个标记点时，就存在$ \ mathsf {k^b（a）} $中的完整异常序列。此外，通过在表面切割上使用感应，我们表征了何时可以将特殊序列完成为完整的特殊序列。如果相关表面的属为零，那么我们表明编织组的作用以及$ \ m athsf {k^b（a）} $中的完整序列的分级转移是传递的。对于较高属的表面的情况，我们将传递性问题减少到存在某些成对异常对象序列的问题。最后，我们解释了使用Koszul二元性在相关对称组中最长元素引起的完整特殊序列的二元性。
In this paper, using the correspondence of gentle algebras and dissections of marked surfaces, we study full exceptional sequences in the perfect derived category $\mathsf{K^b(A)}$ of a gentle algebra $\mathsf{A}$. We show that full exceptional sequences in $\mathsf{K^b(A)}$ exist if and only if the associated marked surface has no punctures and has at least two marked points on the boundary. Furthermore, by using induction on cuts of surfaces, we characterise when an exceptional sequence can be completed to a full exceptional sequence. If the genus of the associated surface is zero then we show that the action of the braid group together with the grading shift on full exceptional sequences in $\mathsf{K^b(A)}$ is transitive. For the case of surfaces of higher genus, we reduce the problem of transitivity to the problem of the existence of certain sequences of pairs of exceptional objects. Finally, we interpret the duality of a full exceptional sequence induced by the longest element in the associated symmetric group using Koszul duality.
