For any simply connected Chevalley group without SL2 factors, the elementary subgroup equals the whole group over Laurent polynomial rings over a special PID, such as the integers.
Abe, Whitehead groups of Chevalley groups over polynomial rings, Comm
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Chevalley groups over Laurent polynomial rings
For any simply connected Chevalley group without SL2 factors, the elementary subgroup equals the whole group over Laurent polynomial rings over a special PID, such as the integers.