Symplectic groups over Laurent polynomial rings and patching diagrams
Fundamentalʹnaâ i prikladnaâ matematika, Tome 5 (1999) no. 3, pp. 943-945
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In this note we prove the following result. Let $A$ be a P.I.D. such that $\operatorname{K}_1\operatorname{Sp}(A)=0$. Then the groups $\operatorname{Sp}_{2r}(A[X_1^{\pm1},\ldots,X_n^{\pm1},Y_1,\ldots,Y_m])$ are generated by elementary symplectic matrices for all integers $r\geq2$.
@article{FPM_1999_5_3_a22,
author = {V. I. Kopeiko},
title = {Symplectic groups over {Laurent} polynomial rings and patching diagrams},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {943--945},
publisher = {mathdoc},
volume = {5},
number = {3},
year = {1999},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_1999_5_3_a22/}
}
V. I. Kopeiko. Symplectic groups over Laurent polynomial rings and patching diagrams. Fundamentalʹnaâ i prikladnaâ matematika, Tome 5 (1999) no. 3, pp. 943-945. http://geodesic.mathdoc.fr/item/FPM_1999_5_3_a22/