Steinberg Group as a Lattice in a lie group
Given an integral domain $R$, the Steinberg group $St_n(R)$ is the group given by generators
Subject to the relations
The Steinberg group is the universal central extension of the special linear group over $R$; $Sl_n(R)$.
Is there a description of the Steinberg group $St_n(Z)$, the special linear group over the integers as a lattice in some lie group, and some covering map realizing the universal central extension of $Sln(R)$ ( real coefficients), which restricts to the integral universal central extension of $Sln(Z)$ given by the Steinberg group ?