Weights in a Benson-Solomon block
Weights in a Benson-Solomon block
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Benson-Solomon 块中的权重
DOI：
10.1017/fms.2023.53
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发表时间：
2023
期刊：
影响因子：
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通讯作者：
Semeraro, Jason
中科院分区：
文献类型：
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作者：
Lynd, Justin;Semeraro, Jason
对于由p-群上的饱和融合系统以及相容的Külshammer-Puig上同调类族组成的每一对，可以计算由这些数据产生的假设块代数中的权重。当权对产生于特征为p的有限群代数的一个真块时，权的共轭类的数目被假定为块中的单模的数目。我们发现，有唯一的这样的对与每个本森-所罗门异国情调的融合系统，并在一个假设的本森-所罗门块的重量的数量是，独立的定义领域。这是进行部分列出明确的共轭所有中心激进的子群和他们的外部自同构群在这些系统。
To each pair consisting of a saturated fusion system over a p-group together with a compatible family of Külshammer-Puig cohomology classes, one can count weights in a hypothetical block algebra arising from these data. When the pair arises from a genuine block of a finite group algebra in characteristic p, the number of conjugacy classes of weights is supposed to be the number of simple modules in the block. We show that there is unique such pair associated with each Benson-Solomon exotic fusion system, and that the number of weights in a hypothetical Benson-Solomon block is , independently of the field of definition. This is carried out in part by listing explicitly up to conjugacy all centric radical subgroups and their outer automorphism groups in these systems.