论文标题
三角形类别之间的绿色对应和相对投影率
Green correspondence and relative projectivity for pairs of adjoint functors between triangulated categories
论文作者
论文摘要
Auslander和Kleiner在1994年证明了三个类别之间的伴随函数的绿色对应的抽象版本。它们产生了某些子类别的添加剂，在模块化表示理论的特殊环境中赋予经典的绿色对应关系。卡尔森（Carlson），彭（Peng）和惠勒（Wheeler）在1998年表明，模块化表示理论的经典环境中的绿色对应关系实际上是三角形类别之间相对于非标准三角结构的等效性。在本说明中，我们首先定义和研究相对投影率的版本，分别相对于伴随函子对的相对注射率。然后，我们修改Auslander Kleiner的构建，以使信函在三角类别的环境中存在。
Auslander and Kleiner proved in 1994 an abstract version of Green correspondence for pairs of adjoint functors between three categories. They produce additive quotients of certain subcategories giving the classical Green correspondence in the special setting of modular representation theory. Carlson, Peng and Wheeler showed in 1998 that Green correspondence in the classical setting of modular representation theory is actually an equivalence between triangulated categories with respect to a non standard triangulated structure. In the present note we first define and study a version of relative projectivity, respectively relative injectivity with respect to pairs of adjoint functors. We then modify Auslander Kleiner's construction such that the correspondence holds in the setting of triangulated categories.
