On the group sheaf of A-symplectomorphisms

Abstract

This is a part of a further undertaking to affirm that most of classical module theory may be retrieved in the framework of Abstract Differential Geometry (`a la Mallios). More precisely, within this article, we study some defining basic concepts of symplectic geometry on free A-modules by focussing in particular on the group sheaf of A-symplectomorphisms, where A is assumed to be a torsion-free PID C-algebra sheaf. The main result arising hereby is that A-symplectomorphisms locally are products of symplectic transvections, which is a particularly well-behaved counterpart of the classical result.