We describe the structure of the Lie groups endowed with a leftinvariant symplectic form, called symplectic Lie groups, in terms of semi-direct products of Lie groups, symplectic reduction and principal bundles with affine fiber. This description is particularly nice if the group is Hamiltonian, that is, if the left canonical action of the group on itself is Hamiltonian. The principal tool used...

In this paper, we investigate the connection between closed Newton-Cotes formulae, trigonometrically-fitted methods, symplectic integrators and efficient integration of the Schr¨odinger equation. The study of multistep symplectic integrators is very poor although in the last decades several one step symplectic integrators have been produced based on symplectic geometry (see the relevant lit...

in this paper we first construct the non-split extension $overline{g}= 2^{6} {^{cdot}}sp(6,2)$ as a permutation group acting on 128 points. we then determine the conjugacy classes using the coset analysis technique, inertia factor groups and fischer matrices, which are required for the computations of the character table of $overline{g}$ by means of clifford-fischer theory. there are two inerti...