SU(3) as a 2-plectic manifold

The Killing form induces a 2-plectic structure on a compact semisimple Lie group. The associated Lie group of canonical transformations (2-plectomorphisms) is compact. This 2-plectic structure induces a Cartan connection on the Lie group. The curvature and torsion tensor of this connection have been calculated for the special unitary Lie group SU(3). It is shown that the homogeneous spaces SU(3)SU(2), SU(3)S1 and SU(3)T2 also, admit 2-plectic structures, which are induced by closed left invariant 3-forms on SU(3), whereas SU(3)U(2) and SU(3)SO(3) do not admit such 2-plectic structures.