2-Calabi-Yau范畴的环簇结构
Cluster structures from 2-Calabi-Yau categories with loops
摘要：
我们概括的概念集群结构的Buan Iyama-Reiten-斯科特的工作，包括情况下，自同态环的集群可能有循环。证明了在Hom有限2-Calabi-Yau范畴中，当极大刚性对象的自同态环的箭图中不存在2-圈时，极大刚性对象的集合满足这些公理。我们将这一结果应用到簇范畴的管，并表明，这一类形成了一个很好的模型的组合B型集群代数。
英文摘要：
We generalise the notion of cluster structures from the work of Buan-Iyama-Reiten-Scott to include situations where the endomorphism rings of the clusters may have loops. We show that in a Hom-finite 2-Calabi-Yau category, the set of maximal rigid objects satisfies these axioms whenever there are no 2-cycles in the quivers of their endomorphism rings. We apply this result to the cluster category of a tube, and show that this category forms a good model for the combinatorics of a type B cluster algebra.
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