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

Abstract

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