Chevalley groups of polynomial rings over Dedekind domains
K-Theory and Homology
2019-06-26 v2 Group Theory
Abstract
Let R be a Dedekind domain, and let G be a simply connected Chevalley-Demazure group scheme of rank =>2. We prove that G(R[x_1,...,x_n])=G(R)E(R[x_1,...,x_n]) for any n=>1. This extends the corresponding results of A. Suslin and F. Grunewald, J. Mennicke, and L. Vaserstein for G=SL_n, Sp_2n. We also deduce some corollaries of the above result for regular rings R of higher dimension and discrete Hodge algebras over R.
Cite
@article{arxiv.1812.04326,
title = {Chevalley groups of polynomial rings over Dedekind domains},
author = {Anastasia Stavrova},
journal= {arXiv preprint arXiv:1812.04326},
year = {2019}
}