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 -