论文标题
$ p $ - 代数块之间的等价
$p$-permutation equivalences between blocks of group algebras
论文作者
论文摘要
我们将两个$ p $ P $ - blocks $ a $ a $和$ b $的有限组$ g $和$ h $之间的{$ p $ - permuart等价的概念扩展到[boltje-xu 2008]的定义到虚拟$ p $ p $ p $ -pperm-perm-perm-perm-pontim-nimpont bimodule，其组件具有扭曲的diagonal Vertices。结果表明，保留了$ a $ a和$ b $的各种不变性，包括缺陷组，融合系统和külshammer-puig类。此外，这表明$ p $ permution等价具有其他令人惊讶的属性。他们只有一个具有最大顶点的组成部分，而$ p $ py-permunt的等价之间的$ a $ a和$ b $是有限的（可能是空的）。 The paper uses new methods: a consequent use of module structures on subgroups of $G\times H$ arising from Brauer constructions which in general are not direct product subgroups, the necessary adaptation of the notion of tensor products between bimodules, and a general formula (stated in these new terms) for the Brauer construction of a tensor product of $p$-permutation bimodules.
We extend the notion of a {$p$-permutation equivalence} between two $p$-blocks $A$ and $B$ of finite groups $G$ and $H$, from the definition in [Boltje-Xu 2008] to a virtual $p$-permutation bimodule whose components have twisted diagonal vertices. It is shown that various invariants of $A$ and $B$ are preserved, including defect groups, fusion systems, and Külshammer-Puig classes. Moreover it is shown that $p$-permutation equivalences have additional surprising properties. They have only one constituent with maximal vertex and the set of $p$-permutation equivalences between $A$ and $B$ is finite (possibly empty). The paper uses new methods: a consequent use of module structures on subgroups of $G\times H$ arising from Brauer constructions which in general are not direct product subgroups, the necessary adaptation of the notion of tensor products between bimodules, and a general formula (stated in these new terms) for the Brauer construction of a tensor product of $p$-permutation bimodules.
