Research output: Contribution to journal › Article › peer-review
Chevalley groups of polynomial rings over Dedekind domains. / Stavrova, Anastasia.
In: Journal of Group Theory, Vol. 23, No. 1, 01.2019.Research output: Contribution to journal › Article › peer-review
}
TY - JOUR
T1 - Chevalley groups of polynomial rings over Dedekind domains
AU - Stavrova, Anastasia
N1 - ournal of Group Theory, Volume 23, Issue 1, Pages 121–132, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: https://doi.org/10.1515/jgth-2019-0100.
PY - 2019/1
Y1 - 2019/1
N2 - Let R be a Dedekind domain and G a split reductive group, i.e. a Chevalley-Demazure group scheme, of rank ≥ 2 {geq 2}. We prove that G ? (R ? [ x 1, ..., x n ]) = G ? (R) ? E ? (R ? [ x 1, ..., x n ]) ? for any ? n ≥ 1. G(R[x-{1},ldots,x-{n}])=G(R)E(R[x-{1},ldots,x-{n}])quadtext{for any} n% geq 1. In particular, this extends to orthogonal groups the corresponding results of A. Suslin and F. Grunewald, J. Mennicke and L. Vaserstein for G = SL N, Sp 2 ? N {G=mathrm{SL}-{N},mathrm{Sp}-{2N}}. We also deduce some corollaries of the above result for regular rings R of higher dimension and discrete Hodge algebras over R.
AB - Let R be a Dedekind domain and G a split reductive group, i.e. a Chevalley-Demazure group scheme, of rank ≥ 2 {geq 2}. We prove that G ? (R ? [ x 1, ..., x n ]) = G ? (R) ? E ? (R ? [ x 1, ..., x n ]) ? for any ? n ≥ 1. G(R[x-{1},ldots,x-{n}])=G(R)E(R[x-{1},ldots,x-{n}])quadtext{for any} n% geq 1. In particular, this extends to orthogonal groups the corresponding results of A. Suslin and F. Grunewald, J. Mennicke and L. Vaserstein for G = SL N, Sp 2 ? N {G=mathrm{SL}-{N},mathrm{Sp}-{2N}}. We also deduce some corollaries of the above result for regular rings R of higher dimension and discrete Hodge algebras over R.
UR - http://www.scopus.com/inward/record.url?scp=85072629915&partnerID=8YFLogxK
U2 - 10.1515/jgth-2019-0100
DO - 10.1515/jgth-2019-0100
M3 - Article
AN - SCOPUS:85072629915
VL - 23
JO - Journal of Group Theory
JF - Journal of Group Theory
SN - 1433-5883
IS - 1
ER -
ID: 47578942