A Simple Model of Double Dynamics on Lie Groups

Abstract: 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 Drinfeldd 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.