Explicit presentation of relative Steinberg groups

Abstract

We find an explicit presentation of relative linear Steinberg groups $\mathrm{St}(n,R,I)$ for any ring $R$ and $n\ge 4$ by generators and relations as abstract groups. We also prove a similar result for relative simply laced Steinberg groups $\mathrm{St}(\Phi ;R,I)$ for commutative $R$ and $\Phi \in \{{\mathsf{A}}_{\ell },{\mathsf{D}}_{\ell },{\mathsf{E}}_{\ell }\mid \ell \ge 3\}$.

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• Centrality of ${\mathrm{K}}_2$-functor revisited
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• Commutators of relative and unrelative elementary unitary groups
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Cited by in corpus (1)

• A presentation of relative unitary Steinberg groups