2023/08/02 by Voronetsky, Egor
#20G99 #FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.2308.01225
Isotropic odd unitary groups generalize Chevalley groups of classical types over commutative rings and their twisted forms. Such groups have root subgroups parameterized by a root system BC_ℓ and may be constructed by so-called odd form rings with Peirce decompositions. We show the converse: if a group G has root subgroups indexed by roots of BC_ℓ and satisfying natural conditions, then there is a homomorphism StU(R, Δ) → G inducing isomorphisms on the root subgroups, where StU(R, Δ) is the odd unitary Steinberg group constructed by an odd form ring (R, Δ) with a Peirce decomposition. For groups with root subgroups indexed by \mathsf A_ℓ (the already known case) the resulting odd form ring is essentially a generalized matrix ring.