FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1995, VOLUME 1, NUMBER 2, PAGES 545-548

On the structure of the symplectic group over polynomial rings with regular coefficients

V.I.Kopeiko

In this note we prove the following result. Let A be a ring of the geometric type or A = C [[T₁,..., T_m]], where C is a regular ring and $\dim C \leq 1$. Then the group Sp_2r (A [X₁,...,X_n]) ($r \geq 2$) is generated by elementary symplectic matrices.

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Last modified: October 7, 1997.