论文标题
遗传代数模块类别的图像扩展封闭的子类别
Image-extension-closed subcategories of module categories of hereditary algebras
论文作者
论文摘要
我们研究了模块类别的IE关闭子类别，这些子类别在拍摄图像和扩展下关闭。我们研究了IE关闭的子类别和扭转对之间的关系，并使用IE封闭的子类别来表征$τ$的有限代数。对于遗传病例，我们表明可以通过双刚性模块，成对满足某些同源条件的刚性模块来对IE关闭的子类别进行分类。此外，我们类似地引入了双刚性模块的突变，该突变与倾斜模块相似，该模块为代表限制的情况提供了计算所有双刚性模块的方法。
We study IE-closed subcategories of a module category, subcategories which are closed under taking Images and Extensions. We investigate the relation between IE-closed subcategories and torsion pairs, and characterize $τ$-tilting finite algebras using IE-closed subcategories. For the hereditary case, we show that IE-closed subcategories can be classified by twin rigid modules, pairs of rigid modules satisfying some homological conditions. Moreover, we introduce mutation of twin rigid modules analogously to tilting modules, which gives a way to calculate all twin rigid modules for the representation-finite case.
