English

Centralizer of the elementary subgroup of an isotropic reductive group

Algebraic Geometry 2010-12-14 v2 Group Theory

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_{R_M} 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.

Keywords

Cite

@article{arxiv.1012.0278,
  title  = {Centralizer of the elementary subgroup of an isotropic reductive group},
  author = {Ekaterina Kulikova and Anastasia Stavrova},
  journal= {arXiv preprint arXiv:1012.0278},
  year   = {2010}
}

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7 pages