论文标题
支持$τ$的突变图 - 偏斜式代数上的模块
Mutation graph of support $τ$-tilting modules over a skew-gentle algebra
论文作者
论文摘要
令$ \ Mathcal {d} $为Hom-Finite，Krull-Schmidt，2-Calabi-yau三角式类别，具有刚性对象$ r $。令$λ= \ operatoTorname {end} _ {\ Mathcal {d}} r $为$ r $的内态代数。我们通过Exchange Triangles在两项子类别$ r \ ast r [1] $中介绍了最大刚性对象突变的概念，该$ r \ ast r [1] $概念与支持$λ$ -Modules的支持$τ$的突变兼容。如果$ \ Mathcal {d} $是由刺穿的标记表面引起的群集类别，则表明，支持$τ$的突变图$λ$ - 模块是同构的，对于某些标记的弧线集的flips图表，该图的表面上已连接，该表面已连接。作为一个直接结果，连接了支撑$τ$的突变图。
Let $\mathcal{D}$ be a Hom-finite, Krull-Schmidt, 2-Calabi-Yau triangulated category with a rigid object $R$. Let $Λ=\operatorname{End}_{\mathcal{D}}R$ be the endomorphism algebra of $R$. We introduce the notion of mutation of maximal rigid objects in the two-term subcategory $R\ast R[1]$ via exchange triangles, which is shown to be compatible with mutation of support $τ$-tilting $Λ$-modules. In the case that $\mathcal{D}$ is the cluster category arising from a punctured marked surface, it is shown that the graph of mutations of support $τ$-tilting $Λ$-modules is isomorphic to the graph of flips of certain collections of tagged arcs on the surface, which is moreover proved to be connected. As a direct consequence, the mutation graph of support $τ$-tilting modules over a skew-gentle algebra is connected.
