Another presentation of orthogonal Steinberg groups

Abstract

We use the pro-group approach to show that $\mathrm{StO}(M,q)$ admits van der Kallen's "another presentation", where $M$ is a module over a commutative ring with sufficiently isotropic quadratic form $q$. Moreover, we construct an analog of ESD-transvections in orthogonal Steinberg pro-groups under some assumptions on their parameters.

Minor edits, added reference to author's thesis

References in corpus (4)

• On centrality of $K_2$ for Chevalley groups of type $E_l$
• On centrality of even orthogonal ${\mathrm{K}}_2$
• Centrality of ${\mathrm{K}}_2$-functor revisited
• Stability for odd unitary $K_1$