Steinberg group

Summary

The Steinberg group $St(R)$ of a ring $R$ is the group generated by symbols $x_{ij}(r)$ subject only to the Steinberg relations. It maps onto the group $E(R)$ generated by elementary matrices, and the kernel of this map is $K_2(R)$. This map is the universal central extension of $E(R)$, which makes the Steinberg group the natural home of $K_2$.