TY - JOUR

T1 - Groups with BC_ℓ-commutator relations

AU - Воронецкий, Егор Юрьевич

PY - 2025/7/1

Y1 - 2025/7/1

N2 - 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 BCℓ 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 BCℓ and satisfying natural conditions, then there is a homomorphism [Figure presented] inducing isomorphisms on the root subgroups, where [Figure presented] 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 Aℓ (the already known case) the resulting odd form ring is essentially a generalized matrix ring.

AB - 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 BCℓ 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 BCℓ and satisfying natural conditions, then there is a homomorphism [Figure presented] inducing isomorphisms on the root subgroups, where [Figure presented] 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 Aℓ (the already known case) the resulting odd form ring is essentially a generalized matrix ring.

KW - Classical groups

KW - Groups with commutator relations

KW - Odd unitary groups

KW - Root systems

UR - https://www.mendeley.com/catalogue/3655de21-a0f2-38c1-96a7-62cae27208e9/

U2 - 10.1016/j.jpaa.2025.107966

DO - 10.1016/j.jpaa.2025.107966

M3 - Article

VL - 229

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 7

M1 - 107966

ER -