论文标题
关于Auslander-Kleiner的绿色信件的三角版本的评论
Remarks on a triangulated version of Auslander-Kleiner's Green correspondence
论文作者
论文摘要
For a finite group $G$ and an algebraically closed field $k$ of characteristic $p>0$ for any indecomposable finite dimensional $kG$-module $M$ with vertex $D$ and a subgroup $H$ of $G$ containing $N_G(D)$ there is a unique indecomposable $kH$-module $N$ of vertex $D$ being a direct summand of the restriction of $ m $至$ h $。 Auslander-Kleiner推广到添加剂类别之间的伴随函数对的情况，称为绿色对应。在组环的最初情况下，卡尔森·潘克轮（Carlson-Peng-Wheeler）证明，这种对应关系实际上是对相应模块类别的三角形商类别之间三角函数的限制。我们回顾了这一理论，并展示了我们如何使用Verdier本地化对Auslander-Kleiner和Carlson-Peng-Wheeler的方法进行共同的概括。
For a finite group $G$ and an algebraically closed field $k$ of characteristic $p>0$ for any indecomposable finite dimensional $kG$-module $M$ with vertex $D$ and a subgroup $H$ of $G$ containing $N_G(D)$ there is a unique indecomposable $kH$-module $N$ of vertex $D$ being a direct summand of the restriction of $M$ to $H$. This correspondence, called Green correspondence, was generalised by Auslander-Kleiner to the situation of pairs of adjoint functors between additive categories. In the original situation of group rings Carlson-Peng-Wheeler proved that this correspondence is actually restriction of triangle functors between triangulated quotient categories of the corresponding module categories. We review this theory and show how we got a common generalisation of the approaches of Auslander-Kleiner and Carlson-Peng-Wheeler, using Verdier localisations.
