非交叉二部图的极大刚性对象
Maximal rigid objects as noncrossing bipartite graphs
摘要：
设Q是A型Dynkin算子。Q的路代数的有界导出范畴具有由Auslander-Reiten平移的合成和移位函子的平方给出的自等价。我们在相应的轨道范畴C（Q）的最大刚性对象进行分类，在一个圆的二部不相交图（与循环）。我们还描述了极大刚性对象的自同态代数，并证明了这类代数中的某一类是A型迭代倾斜代数。
英文摘要：
Let Q be a Dynkin quiver of type A. The bounded derived category of the path algebra of Q has an autoequivalence given by the composition of the Auslander-Reiten translate and the square of the shift functor. We classify the maximal rigid objects in the corresponding orbit category C(Q), in terms of bipartite noncrossing graphs (with loops) in a circle. We also describe the endomorphism algebras of the maximal rigid objects, and we prove that a certain class of these algebras are iterated tilted algebras of type A.
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