Spin Calogero models obtained from dynamical r-matrices and geodesic motion

摘要: We study classical integrable systems based on the Alekseev–Meinrenken dynamical r-matrices corresponding to automorphisms of self-dual Lie algebras, G. prove that these are uniquely characterized by a non-degeneracy property and apply construction due Li Xu associate spin Calogero type models with them. The equation motion any model this is found be projection natural geodesic group G algebra G, its phase space interpreted as Hamiltonian reduction an open submanifold cotangent bundle T∗G, using symmetry arising from adjoint action twisted underlying automorphism. This shows integrability resulting gives algorithm solve As illustrative examples we present new built involutive diagram real split compact simple also explain many further fit in r-matrix framework.