离散群对融合系统的可实现性
Realizability of fusion systems by discrete groups
AI总结：
本文研究离散p-挠群上融合系统的可实现性，证明紧李群的融合系统可由线性挠群实现，并提出新工具证明某些融合系统不是序列可实现的，通过两大族例子加以说明。
摘要：
对于素数$p$，离散$p$-挠群上的融合系统是一类范畴，它们以与有限$p$-群上的融合系统模型化并推广有限群的$p$-局部结构相同的方式，模型化并推广李群及某些其他无限群的$p$-局部结构。在有限情形下，若一个融合系统$\mathcal{F}$同构于某个有限群的融合系统，则自然称其为可实现的；但在离散$p$-挠情形下，可实现性的含义则不那么明确。本文考察了离散$p$-挠群上融合系统的若干不同类型的可实现性，包括由线性挠群实现的可实现性和序列可实现性，其中后者最为一般。在证明紧李群的融合系统总是可由线性挠群实现（因此是序列可实现的）之后，我们给出了一些新的工具，用于证明某些融合系统不是序列可实现的，并用两大族例子加以说明。
英文摘要：
For a prime $p$, fusion systems over discrete $p$-toral groups are categories that model and generalize the $p$-local structure of Lie groups and certain other infinite groups in the same way that fusion systems over finite $p$-groups model and generalize the $p$-local structure of finite groups. In the finite case, it is natural to say that a fusion system $\mathcal{F}$ is realizable if it is isomorphic to the fusion system of a finite group, but it is less clear what realizability should mean in the discrete $p$-toral case. In this paper, we look at some of the different types of realizability for fusion systems over discrete $p$-toral groups, including realizability by linear torsion groups and sequential realizability, of which the latter is the most general. After showing that fusion systems of compact Lie groups are always realized by linear torsion groups (hence sequentially realizable), we give some new tools for showing that certain fusion systems are not sequentially realizable, and illustrate it with two large families of examples.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
