On the Structure of Infinitesimal Automorphisms of the Poisson-Lie Group <i>SU</i>(2,R)

Abstract

We study the Poisson-Lie structures on the group SU (2,R). We calculate all Poisson-Lie structures on SU (2,R) through the correspondence with Lie bialgebra structures on its Lie algebra su (2,R). We show that all these structures are linearizable in the neighborhood of the unity of the group SU (2,R). Finally, we show that the Lie algebra consisting of all infinitesimal automorphisms is strictly contained in the Lie algebra consisting of Hamiltonian vector fields.