Structure of Chevalley groups over rings via universal localization
Rings and Algebras
2015-11-24 v5
Abstract
In the current article we study structure of a Chevalley group over a commutative ring . We generalize and improve the following results: (1) standard, relative, and multi-relative commutator formulas; (2) nilpotent structure of [relative] ; (3) bounded word length of commutators. To this end we enlarge the elementary group, construct a generic element for the extended elementary group, and use localization in the universal ring. The key step is a construction of a generic element for a principle congruence subgroup, corresponding to a principle ideal.
Keywords
Cite
@article{arxiv.1303.6082,
title = {Structure of Chevalley groups over rings via universal localization},
author = {Alexei Stepanov},
journal= {arXiv preprint arXiv:1303.6082},
year = {2015}
}