Bn型和Cn型Phan几何的球性及F4型Phan定理
The sphericity of the Phan geometries of type Bn and Cn and the Phan-type theorem of type F4
摘要：
本文采用和改进了Abramenko和Devillers-Köhl-Mühlherr提出的方法，建立了B_n和C_n型Phan几何的球性及其推广。作为应用，我们确定了某些双曲Kac-Moody群的酉形式的有限长.我们还再现了群Sp_{2n}（GF（q^2）[t，t^{-1}]）的酉形式的有限长度.另一个应用是F_4型定理的首次公开证明。在有限单群分类的修正中，本文总结了Phan定理的修正及其对非单群花边图的推广。我们还重现了B_n型和C_n型的n-型定理。
英文摘要：
We adapt and refine methods developed by Abramenko and Devillers--Köhl--Mühlherr in order to establish the sphericity of the Phan geometries of type B_n and C_n, and their generalizations. As an application we determine the finiteness length of the unitary form of certain hyperbolic Kac--Moody groups. We also reproduce the finiteness length of the unitary form of the groups Sp_{2n}(GF(q^2)[t,t^{-1}]). Another application is the first published proof of the Phan-type theorem of type F_4. Within the revision of the classification of the finite simple groups this concludes the revision of Phan's theorems and their extension to the non-simply laced diagrams. We also reproduce the Phan-type theorems of types B_n and C_n.
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。
