Quillen-Suslin theory for a structure theorem for the Elementary Symplectic Group

Abstract

A new set of elementary symplectic elements is described, It is shown that these also generate the elementary symplectic group {\rm ESp}$_{2n}(R)$. These generators are more symmetrical than the usual ones, and are useful to study the action of the elementary symplectic group on unimodular rows. Also, an alternate proof of, {\rm ESp}$_{2n}(R)$ is a normal subgroup of {\rm Sp}$_{2n}(R)$, is shown using the Local Global Principle of D. Quillen for the new set of generators.