Centrality of the congruence kernel for elementary subgroups of Chevalley groups of rank >1 over noetherian rings

Chevalley群中K₂的中心性：一种pro-群方法

Centrality of $\mathrm K_2$ for Chevalley groups: a pro-group approach

针对任意交换环证明K₂(F₄,R)的中心性，从而完成秩≥3根系情形，并用pro-群化的局部化方法构造典范Steinberg同态上的交叉模。

On centrality of $K_2$ for Chevalley groups of type $E_l$

For a root system $Φ$ of type $E_l$ and arbitrary commutative ring $R$ we show that the group $K_2(Φ, R)$ is contained in the centre of the Steinberg group $St(Φ, R)$. In course of the proof we also demonstrate an analogue of Quillen---Suslin local-global principle for $K_2(Φ, R)$.

Laurent多项式环上的Chevalley群

Chevalley groups over Laurent polynomial rings

针对无$SL_2$-因子的单连通Chevalley--Demazure群概形，证明了Laurent多项式环与形式Laurent级数环上对应群商初等子群的映射在特定环条件下的单射性（$n=1$时为同构），并给出PID上的推论，推广了特殊线性群和辛群的相关结果。