Endomorphism Algebras of Maximal Rigid Objects in Cluster Tubes
Endomorphism Algebras of Maximal Rigid Objects in Cluster Tubes
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DOI：
10.1080/00927872.2011.600745
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发表时间：
2010-04
影响因子：
0.7
通讯作者：
D. Yang
中科院分区：
文献类型：
--
作者：
D. Yang
给定簇管的一个极大刚性对象T，我们确定T有限表示的对象，然后使用Keller和Reiten的方法证明T的自同态代数是Gorenstein和有限表示型，首先由Vatne证明。当基场的特征不为3时，这个代数就是具有势的某个颤振的雅可比代数。我们研究当T发生突变时，它是如何随电位变化而颤动的。给出了极大刚体的自同态代数的等价分类。
Given a maximal rigid object T of the cluster tube, we determine the objects finitely presented by T. We then use the method of Keller and Reiten to show that the endomorphism algebra of T is Gorenstein and of finite representation type, as first shown by Vatne. This algebra turns out to be the Jacobian algebra of a certain quiver with potential, when the characteristic of the base field is not 3. We study how this quiver with potential changes when T is mutated. We also provide a derived equivalence classification for the endomorphism algebras of maximal rigid objects.