TITLE:
On the Structure of Infinitesimal Automorphisms of the Poisson-Lie Group SU(2,R)
AUTHORS:
Bousselham Ganbouri
KEYWORDS:
Poisson-Lie Structure, Lie Bialgebra, Hamiltonian, Poisson Automorphism, Linearization
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.4 No.4,
April
9,
2014
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.