FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1999, VOLUME 5, NUMBER 3, PAGES 943-945

Symplectic groups over Laurent polynomial rings and patching diagrams

V. I. Kopeiko

Abstract

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In this note we prove the following result. Let $A$ be a P.I.D. such that $K$₁Sp (A) = 0. Then the groups $Sp$_2r(A[X₁^±1,..., X_n^±1,Y_1,...,Y_m]) are generated by elementary symplectic matrices for all integers $r$³ 2.

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Last modified: November 11, 1999