Joint Invariants of Symplectic and Contact Lie Algebra Actions

Abstract

By restricting generating functions of infinitesimal symmetries of symplectic and contact vector spaces to quadratic forms, we obtain a finite-dimensional Lie subalgebra, consisting of vector fields isomorphic to the linear symplectic or conformal symplectic algebra. This allows us to look for joint invariants of the diagonal action of g on product manifolds. We find an explicit recipe for creating a transcendence basis for the field of m-fold rational joint invariants over R, starting from a base space M of any dimension greater than or equal to 2.