A presentation of relative unitary Steinberg groups

2022/06/23 by Voronetsky, Egor
#19C20 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2206.11885

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_ℓ, \mathsf C_ℓ, \mathsf F₄ for ℓ ≥ 3. For simply laced root systems such result is already known.

Related

• Groups with BC_ℓ-commutator relations
• Another presentation of orthogonal Steinberg groups
• Relative symplectic Steinberg group
• Bounded generation of Steinberg groups over Dedekind rings of arithmetic type
• Cosheaves of Steinberg pro-groups