Levi Decomposition for Carpet Subgroups of Chevalley Groups Over a Field

Abstract

It is proved that a carpet subgroup of a Chevalley group of type Φ over a field is a semidirect product whose kernel is defined by a unipotent carpet of type Φ, while the noninvariant factor is a central product of carpet subgroups each of which is defined by an irreducible subcarpet of type Φi for some indecomposable root subsystem Φ_i of Φ. The obtained result can be viewed as an analog of the Levi decomposition.