Centralizer of the elementary subgroup of an isotropic reductive group

2010/12/01 by Ekaterina Kulikova, Anastasia Stavrova, Kulikova, Ekaterina +1 · 1 citation
Mathematics · #20G07 #20G15 #20G35 #Algebraic Geometry (math.AG) #FOS: Mathematics #Group Theory (math.GR) #math.AG #math.GR #msc:20G07 #msc:20G15 #msc:20G35

paper · pdf · doi:10.48550/arxiv.1012.0278

7 pages

arxiv created 2010/12/11 · arxiv updated 2010/12/14

Abstract

Let G be an isotropic reductive algebraic group over a commutative ring R. Assume that, for any maximal ideal M of R, the rank of the relative root system of G_RM is greater or equal than 2. We show that under this assumption the centralizer of E(R) in G(R) coincides with the abstract group-theoretic center of G(R) and with Cent(G)(R). This generalizes a result of E. Abe and J. Hurley.

Cited by

• Abstract isomorphisms of isotropic root graded groups over rings

Related

• The Diophantine problem in isotropic reductive groups
• Locally isotropic elementary groups
• Elementary subgroup of an isotropic reductive group is perfect
• On the congruence kernel of isotropic groups over rings
• Relative centralisers of relative subgroups