SU(3)as a2-plectic manifold

Abstract

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 S U ( 3 ) . It is shown that the homogeneous spaces S U ( 3 ) S U ( 2 ) , S U ( 3 ) S 1 and S U ( 3 ) T 2 also, admit 2-plectic structures, which are induced by closed left invariant 3-forms on S U ( 3 ) , whereas S U ( 3 ) U ( 2 ) and S U ( 3 ) S O ( 3 ) do not admit such 2-plectic structures.