局部环上${}^2 D_\ell$($\ell \geq 4$)型扭Chevalley群的自同构
Automorphisms of Twisted Chevalley Groups of type ${}^2 D_\ell \ (\ell \geq 4)$ over Local Rings
AI总结:
本文作为交换环上扭Chevalley群同构与自同构分类系列研究的一部分,证明了含1/2的局部环上${}^2 D_\ell$($\ell \geq 4$)型扭Chevalley群的所有自同构均为标准自同构。
AI中文摘要:
本文是致力于交换环上扭Chevalley群的同构与自同构分类的系列研究之一。本工作中,我们证明了含1/2的局部环上${}^2 D_\ell$($\ell \geqslant 4$)型扭Chevalley群的每个自同构都是标准自同构。
英文摘要:
This paper is part of a series devoted to the classification of isomorphisms and automorphisms of twisted Chevalley groups over commutative rings. In this work, we prove that every automorphism of a twisted Chevalley group of type ${}^2 D_\ell$ ($\ell \geqslant 4$) over a local ring containing $1/2$ is standard.