Sbornik. Mathematics, Tome 34 (1978) no. 5, pp. 655-669
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V. I. Kopeiko. The stabilization of symplectic groups over a polynomial ring. Sbornik. Mathematics, Tome 34 (1978) no. 5, pp. 655-669. http://geodesic.mathdoc.fr/item/SM_1978_34_5_a5/
@article{SM_1978_34_5_a5,
author = {V. I. Kopeiko},
title = {The stabilization of symplectic groups over a~polynomial ring},
journal = {Sbornik. Mathematics},
pages = {655--669},
year = {1978},
volume = {34},
number = {5},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1978_34_5_a5/}
}
TY - JOUR
AU - V. I. Kopeiko
TI - The stabilization of symplectic groups over a polynomial ring
JO - Sbornik. Mathematics
PY - 1978
SP - 655
EP - 669
VL - 34
IS - 5
UR - http://geodesic.mathdoc.fr/item/SM_1978_34_5_a5/
LA - en
ID - SM_1978_34_5_a5
ER -
%0 Journal Article
%A V. I. Kopeiko
%T The stabilization of symplectic groups over a polynomial ring
%J Sbornik. Mathematics
%D 1978
%P 655-669
%V 34
%N 5
%U http://geodesic.mathdoc.fr/item/SM_1978_34_5_a5/
%G en
%F SM_1978_34_5_a5
We prove that if $B$ is a polynomial ring over a field, then for $r\geqslant2$, any element of $Sp_{2r}B$ can be written as a product of elementary symplectic matrices over $B$. We also prove a stabilization theorem for the symplectic $K_1$-functor in the case of polynomial rings and Laurent rings. Bibliography: 6 titles.
[2] A. A. Suslin, “O strukture spetsialnoi lineinoi gruppy nad koltsami mnogochlenov”, Izv. AN SSSR, seriya matem., 41 (1977), 503–516 | MR
[3] L. N. Vasershtein, “Stabilizatsiya unitarnykh i ortogonalnykh grupp nad koltsom s involyutsiei”, Matem. sb., 81(123) (1970), 328–351
[4] L. N. Vasershtein, A. A. Suslin, “Problema Serra o proektivnykh modulyakh nad koltsami mnogochlenov i algebraicheskaya $K$-teoriya”, Izv. AN SSSR, seriya matem., 40 (1976), 993–1055
[5] X. Base, Dzh. Milnor, Zh.-P. Serr, “Reshenie kongruents-problemy dlya $SL_n(n\ge 3)$ i $Sp_{2n}(n\ge 2)$”, Matematika, 15:1 (1971), 44–60
