A new set of elementary symplectic elements is described. It is shown that these also generate the elementary symplectic group $ESp_{2n}(R)$. 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, $ESp_{2n}(R) is a normal subgroup of $Sp_{2n}(R)$, is shown using the Local Global Principle of D. Quillen for the new set of generators.
Quillen-Suslin theory for a structure theorem for the elementary symplectic group
KUMAR, NEERAJ;
2013-01-01
Abstract
A new set of elementary symplectic elements is described. It is shown that these also generate the elementary symplectic group $ESp_{2n}(R)$. 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, $ESp_{2n}(R) is a normal subgroup of $Sp_{2n}(R)$, is shown using the Local Global Principle of D. Quillen for the new set of generators.
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