On Modules over Endomorphism Algebras of Maximal Rigid Objects in 2-Calabi-Yau Triangulated Categories
On Modules over Endomorphism Algebras of Maximal Rigid Objects in 2-Calabi-Yau Triangulated Categories
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DOI：
10.1080/00927872.2013.809531
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发表时间：
2014-05
影响因子：
0.7
通讯作者：
Pin Liu;Yunli Xie
中科院分区：
文献类型：
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作者：
Pin Liu;Yunli Xie
本文研究了2-Calabi-Yau三角范畴中极大刚性对象的自同态代数上的模。研究了几乎完全倾斜模的可能补。结合Happel定理，我们证明了这类代数上的倾斜模的可能交换序列是由相应的2-Calabi-Yau三角化范畴中的极大刚性对象的交换三角形诱导的.对于无限投射维数的模，推广了Beaudet-Brüstle-Todorov关于簇倾斜代数的一个结果.
This note investigates the modules over the endomorphism algebras of maximal rigid objects in 2-Calabi-Yau triangulated categories. We study the possible complements for almost complete tilting modules. Combining with Happel's theorem, we show that the possible exchange sequences for tilting modules over such algebras are induced by the exchange triangles for maximal rigid objects in the corresponding 2-Calabi-Yau triangulated categories. For the modules of infinite projective dimension, we generalize a recent result by Beaudet–Brüstle–Todorov for cluster-tilted algebras.