A Quaternionic Structure as a Landmark for Symplectic Maps

TL;DR

This paper introduces a quaternionic structure on the product of symplectic manifolds to connect Liouvillian forms with linear symplectic maps via the symplectic Cayley's transformation.

Contribution

It presents a novel quaternionic framework that links Liouvillian forms to symplectic maps, enhancing understanding of symplectic geometry.

Findings

Establishes a quaternionic structure on symplectic manifold products.

Relates Liouvillian forms to linear symplectic maps.

Utilizes symplectic Cayley's transformation for this relation.

Abstract

We use a quaternionic structure on the product of two symplectic manifolds for relating Liouvillian forms with linear symplectic maps obtained by the symplectic Cayley's transformation.