Explicit presentation of relative Steinberg groups

Abstract

We find an explicit presentation of relative linear Steinberg groups St(n, R, I) for any ring R and n ≥ 4 by generators and relations as abstract groups. We also prove a similar result for relative simply laced Steinberg groups St(Φ; R, I) for commutative R and Φ ∈ {A ℓ , D ℓ , E ℓ | ℓ ≥ 3}.