论文标题
融合系统上的以Mackey函数为中心的绿色通信
Green correspondence on centric Mackey functor over fusion systems
论文作者
论文摘要
在本文中，我们对（中心）Mackey Foundor进行了融合系统的定义，该系统将Mackey Foundor的概念在组上概括。在这种情况下，我们证明，鉴于相关环上的某些条件，融合系统（由Diaz和Libman所定义）上的中心伯侧环对任何中心的Mackey函数作用。我们还证明，绿色对应是为了融合系统而定于融合系统的绿色对应。作为证明这一点的一种手段，我们介绍了中心的Mackey函数对融合系统的相对投影率的概念，并在$ \ Mathcal {o} \ left中提供特定产品的分解（\ Mathcal {f}^c \ right）_ {\ sqcup} $ $ \ MATHCAL {O} \ left（n _ {\ Mathcal {f}}} \ left（h \ right）^c \ right）_ {\ sqcup} $。
In this paper we give a definition of (centric) Mackey functor over a fusion system which generalizes the notion of Mackey functor over a group. In this context we prove that, given some conditions on a related ring, the centric Burnside ring over a fusion system (as defined by Diaz and Libman) acts on any centric Mackey functor. We also prove that the Green correspondence holds for centric Mackey functors over fusion systems. As a means to prove this we introduce a notion of relative projectivity for centric Mackey functors over fusion systems and provide a decomposition of a particular product in $\mathcal{O}\left(\mathcal{F}^c\right)_{\sqcup}$ in terms of the product in $\mathcal{O}\left(N_{\mathcal{F}}\left(H\right)^c\right)_{\sqcup}$.
