A presentation of relative unitary Steinberg groups

Abstract

We find an explicit presentation of relative odd unitary Steinberg groups constructed by odd form rings and of relative doubly laced Steinberg groups over commutative rings, i.e. the Steinberg groups associated with the Chevalley group schemes of the types ${\mathsf{B}}_{\ell }$, ${\mathsf{C}}_{\ell }$, ${\mathsf{F}}_4$ for $\ell \ge 3$. For simply laced root systems such result is already known.

Added section 8 (a presentation for "even" unitary groups, including symplectic and even orthogonal groups)

References in corpus (4)

• Centrality of ${\mathrm{K}}_2$-functor revisited
• Explicit presentation of relative Steinberg groups
• Twisted forms of classical groups
• On the ${\mathbb{A}}^1$-invariance of ${\mathrm{K}}_2$ modeled on linear and even orthogonal groups