Galois G-covering of quotients of linear categories
Galois G-covering of quotients of linear categories
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线性范畴商的伽罗瓦 G 覆盖
DOI：
10.1016/j.jpaa.2022.107244
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发表时间：
2022
影响因子：
0.8
通讯作者：
Panyue Zhou
中科院分区：
文献类型：
--
作者：
Yonggang Hu;Panyue Zhou
本文引入了G-可提理想的概念，推广了Assem和Le Meur定义的可提理想。刻画了g-可提升理想，并构造了与g-可提升理想相关的范畴的商的GaloisG-覆盖。特别地，我们研究了G-可提升可容许理想在GaloisG-覆盖下的行为。进一步，我们证明了局部有界线性范畴上的有限维射影模生成的理想是可容许的G-可提理想。作为应用，我们给出了处理Gorenstein射影对象稳定范畴中Serre函子存在性的约简方法。
In this paper, we introduce the notion ofG-liftable ideals, which extends the liftable ideas defined by Assem and Le Meur. We characterize theG-liftable ideals and construct the GaloisG-coverings of quotients of categories associated to theG-liftable ideals. In particular, we study the behavior ofG-liftable admissible ideals under GaloisG-coverings. Furthermore, we show that the ideals generated by finite dimensional projective modules over a locally bounded linear categories are admissibleG-liftable ideals. As an application, we provide a reduction technique for dealing with the existence of Serre functors in the stable categories of Gorenstein projective objects.
影响因子：
1.7
作者：
Erik Darpo;O. Iyama
通讯作者：
Erik Darpo;O. Iyama