English

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.

Keywords

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}
}