由非交换计数产生的更多有限集
More finite sets coming from non-commutative counting
摘要：
在我们以前的文章中，我们介绍了范畴不变量，它是，粗略地说，在一个给定的三角范畴和它们的同分三角范畴的集合。这里是扩展的例子列表，其中这些集合是有限的。利用Geigle，Lenzning，Meltzer，Hübner关于加权射影线的结果，我们证明了对于任意两个仿射非循环箭图$Q$，$Q'$（即推广的Dynkin型箭图），$D^b(Rep_{\mathbb K}(Q))$中只有1000个完全三角形化子范畴等价于$D^b(Rep_{\mathbb K}(Q'))$，其中${\mathbb K}$是代数闭域.在这些有限集合的元素计数的一些数字是明确确定的。
英文摘要：
In our previous papers we introduced categorical invariants, which are, roughly speaking, sets of triangulated subcategories in a given triangulated category and their quotients. Here is extended the list of examples, where these sets are finite. Using results by Geigle, Lenzning, Meltzer, Hübner for weighted projective lines we show that for any two affine acyclic quivers $Q$, $Q'$ (i.e. quivers of extended Dynkin type) there are only finitely many full triangulated subctegories in $D^b(Rep_{\mathbb K}(Q))$, which are equivalent to $D^b(Rep_{\mathbb K}(Q'))$, where ${\mathbb K}$ is an algebraically closed field. Some of the numbers counting the elements in these finite sets are explicitly determined.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
