A Simple Model of Double Dynamics on Lie Groups

We study the dynamics of the rigid rotator on the group manifold of SU(2) as an instance of dynamics on Lie groups together with a dual model whose carrier space is the Borel group SB(2, C), the Lie Poisson dual of SU(2). We thus introduce a parent action on the Drinfel'd double of the above mentioned groups, which describes the dynamics of a system with twice as many degrees of freedom as the two starting partners. Through a gauging procedure of its global symmetries both the rigid rotor and the dual model are recovered.