论文标题
识别Scott模块的Brauer的不可分解性
Recognition of Brauer indecomposability for a Scott module
论文作者
论文摘要
我们提供了一种方便的方式，以使$ kg $ -scott模块带有顶点$ p $保持不可兼容，这是在任何子组$ q $ of $ p $ as as $ k [q \，c_g（q）] $ - 模块中，$ k $ k $的特征性$ p> 0 $ $ k $。动机是，$ p $ permuntimodule的不可分解性是通过利用粘合方法来获得出色稳定稳定等效性的关键步骤之一，然后可以将其提升到出色的派生等效性。此外，我们的结果解释了Scott模块在Ishioka最近的示例中失败的Brauer Indodocsosible的隐藏原因。
We give a handy way to have a situation that the $kG$-Scott module with vertex $P$ remains indecomposable under taking the Brauer construction for any subgroup $Q$ of $P$ as $k[Q\,C_G(Q)]$-module, where $k$ is a field of characteristic $p>0$. The motivation is that the Brauer indecomposability of a $p$-permutation bimodule is one of the key steps in order to obtain a splendid stable equivalence of Morita type by making use of the gluing method, that then can possibly lift to a splendid derived equivalence. Further our result explains a hidden reason why the Brauer indecomposability of the Scott module fails in Ishioka's recent examples.
