TY - JOUR

T1 - Bruhat Decomposition for Carpet Subgroups of Chevalley Groups Over Fields

AU - Nuzhin, Ya N.

AU - Stepanov, A. V.

PY - 2021/11/1

Y1 - 2021/11/1

N2 - Necessary and sufficient conditions for a Bruhat decomposition to exist in a carpet subgroup of the Chevalley group over a field defined by an irreducible closed carpet of additive subgroups are established. It turns out that carpet subgroups, which admit the Bruhat decomposition and are distinct from Chevalley groups, are exhausted by groups lying between Chevalley groups of types Bl, Cl, F4 or G2 over various imperfect fields of exceptional characteristics 2 or 3, respectively, of which the larger field is an algebraic extension of the smaller field.

AB - Necessary and sufficient conditions for a Bruhat decomposition to exist in a carpet subgroup of the Chevalley group over a field defined by an irreducible closed carpet of additive subgroups are established. It turns out that carpet subgroups, which admit the Bruhat decomposition and are distinct from Chevalley groups, are exhausted by groups lying between Chevalley groups of types Bl, Cl, F4 or G2 over various imperfect fields of exceptional characteristics 2 or 3, respectively, of which the larger field is an algebraic extension of the smaller field.

KW - Bruhat decomposition

KW - carpet subgroup

KW - Chevalley group

UR - http://www.scopus.com/inward/record.url?scp=85120567581&partnerID=8YFLogxK

U2 - 10.1007/s10469-021-09658-4

DO - 10.1007/s10469-021-09658-4

M3 - Article

AN - SCOPUS:85120567581

VL - 60

SP - 327

EP - 335

JO - Algebra and Logic

JF - Algebra and Logic

SN - 0002-5232

IS - 5

ER -