Equivalences between blocks of cohomological Mackey algebras
Equivalences between blocks of cohomological Mackey algebras
复制标题
上同调 Mackey 代数块之间的等价
DOI：
10.1007/s00209-015-1431-x
复制
发表时间：
2014
影响因子：
0.8
通讯作者：
Baptiste Rognerud
中科院分区：
文献类型：
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作者：
Baptiste Rognerud
设是一个有限群，是一个足够大的-模系。莱托群代数的块与所谓上同调Mackey代数的中心本原幂等元（块）之间存在双射。在这里，我们引入了可渗透导出等价的概念，并证明了群代数的两个块之间的可渗透导出等价蕴涵了上同调Mackey代数的对应块之间的导出等价的存在性.特别地，在Broué的Abel亏群猜想的背景下，如果两个块是完全导出等价的，则上同调Mackey代数的相应块是导出等价的.
Letbe a finite group andbe a-modular system which is large enough. Letor. There is a bijection between the blocks of the group algebraand the central primitive idempotents (the blocks) of the so-called cohomological Mackey algebra. Here, we introduce the notion ofpermeablederived equivalence and we prove that a permeable derived equivalence between two blocks of group algebras implies the existence of a derived equivalence between the corresponding blocks of cohomological Mackey algebras. In particular, in the context of Broué’s abelian defect group conjecture, if two blocks aresplendidlyderived equivalent, then the corresponding blocks of cohomological Mackey algebras are derived equivalent.