论文标题
对温和代数的扭转类别分类
Classifying torsion classes of gentle algebras
论文作者
论文摘要
对于有限维柔和的代数，已经知道，可以使用组合解释（称为最大的非划分串组，相应的支撑$τ$）使用的组合解释（称为最大的非交叉串），可以使用合并式的非交叉串行（或等效地构成双期式的complecters）进行分类。在通过明显表面对温和代数的拓扑解释中，可以将这种集合解释为解剖（或部分三角剖分），或者等效地，不包含封闭曲线的层压板。我们将完善这种组合学，这使我们可以在有限长度模块的类别中分类（可能是无限维度）温和的代数。结果，我们的结果还统一了有限维柔性代数的功能有限的扭转类分类，其中某些特殊的双式代数（例如Brauer图代数）。
For a finite-dimensional gentle algebra, it is already known that the functorially finite torsion classes of its category of finite-dimensional modules can be classified using a combinatorial interpretation, called maximal non-crossing sets of strings, of the corresponding support $τ$-tilting module (or equivalently, two-term silting complexes). In the topological interpretation of gentle algebras via marked surfaces, such a set can be interpreted as a dissection (or partial triangulation), or equivalently, a lamination that does not contain a closed curve. We will refine this combinatorics, which gives us a classification of torsion classes in the category of finite length modules over a (possibly infinite-dimensional) gentle algebra. As a consequence, our result also unifies the functorially finite torsion class classification of finite-dimensional gentle algebras with certain classes of special biserial algebras - such as Brauer graph algebras.
