论文标题
突变和扭转对
Mutation and torsion pairs
论文作者
论文摘要
紧凑的淤泥对象的突变是有限维代数的表示理论的基本操作，因为它与群集理论的联系以及与模块或派生类别中的扭转对晶格的联系。在本文中，我们在三角剖分类别中更广泛的淤积或固定T结构框架中发展了突变理论。我们表明，纯净的固定物体的突变涵盖了紧凑型淤积复合物突变的经典概念。作为一种应用，我们证明，在Artinian环上有限生成的模块类别中的任何最小包含扭转类别都对应于不可约突变。这概括为有限的扭转类别的众所周知的结果。
Mutation of compact silting objects is a fundamental operation in the representation theory of finite-dimensional algebras due to its connections to cluster theory and to the lattice of torsion pairs in module or derived categories. In this paper we develop a theory of mutation in the broader framework of silting or cosilting t-structures in triangulated categories. We show that mutation of pure-injective cosilting objects encompasses the classical concept of mutation for compact silting complexes. As an application we prove that any minimal inclusion of torsion classes in the category of finitely generated modules over an artinian ring corresponds to an irreducible mutation. This generalises a well-known result for functorially finite torsion classes.
