论文标题
克利福德的轨道类别定理
Clifford's theorem for orbit categories
论文作者
论文摘要
克利福德理论将有限基团的表示理论与固定正常亚组的表示理论通过诱导和限制，这是一对函子。我们将此结果概括为Krull-Schmidt类别的情况，有限群体起着自动形态为单位。然后，这提供了Cibils和Marcos引入的轨道类别，并在群集代数的背景下以及在Galois涵盖函数的背景下进行了深入研究。我们根据有限的$γ$自动形态的$γ$制定并证明克利夫德定理的krull-schmidt轨道类别，以这种方式阐明了原始类别中不可分解的对象的图像在轨道类别中分解。一对伴随函子似乎是$γ$给出的自然出现的单元的Kleisli类别。
Clifford theory relates the representation theory of finite groups to those of a fixed normal subgroup by means of induction and restriction, which is an adjoint pair of functors. We generalize this result to the situation of a Krull-Schmidt category on which a finite group acts as automorphisms. This then provides the orbit category introduced by Cibils and Marcos, and studied intensively by Keller in the context of cluster algebras, and by Asashiba in the context of Galois covering functors. We formulate and prove Clifford's theorem for Krull-Schmidt orbit categories with respect to a finite group $Γ$ of automorphisms, clarifying this way how the image of an indecomposable object in the original category decomposes in the orbit category. The pair of adjoint functors appears as the Kleisli category of the naturally appearing monad given by $Γ$.
