English

A presentation of relative unitary Steinberg groups

Group Theory 2026-05-08 v3

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 B\mathsf B_\ell, C\mathsf C_\ell, F4\mathsf F_4 for 3\ell \geq 3. For simply laced root systems such result is already known.

Keywords

Cite

@article{arxiv.2206.11885,
  title  = {A presentation of relative unitary Steinberg groups},
  author = {Egor Voronetsky},
  journal= {arXiv preprint arXiv:2206.11885},
  year   = {2026}
}

Comments

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