论文标题
Chevalley组的$ \ Mathrm k_2 $的中心性：一种亲组方法
Centrality of $\mathrm K_2$ for Chevalley groups: a pro-group approach
论文作者
论文摘要
我们证明了$ \ mathrm {k} _2（\ mathsf {f} _4，\，r）$的中心性。这完成了$ \ mathrm k_2（φ，\，r）$的中心性证明，任何根系$ \ geq 3 $。我们的证明仅使用基本定位技术根据亲群体进行了重新重新制定。本文的另一个新结果是在规范同构$ \ mathrm {st}（φ，r）\ to \ mathrm {g} _ \ mathrm {sc}（sc}（φ，r）$中，构建一个交叉模块（φ，r）\ to \ mathrm {g} _ \ mathrm {g} _ \ mathrm {sc} $，尚未以非凡的$ $ $φ$而闻名。
We prove the centrality of $\mathrm{K}_2 (\mathsf{F}_4, \,R)$ for an arbitrary commutative ring $R$. This completes the proof of the centrality of $\mathrm K_2(Φ,\, R)$ for any root system $Φ$ of rank $\geq 3$. Our proof uses only elementary localization techniques reformulated in terms of pro-groups. Another new result of the paper is the construction of a crossed module on the canonical homomorphism $\mathrm{St}(Φ, R) \to \mathrm{G}_\mathrm{sc}(Φ, R)$, which has not been known previouly for exceptional $Φ$.
