%0 Journal Article
%T On the Structure of Infinitesimal Automorphisms of the Poisson-Lie Group <i>SU</i>(2,R)
%A Bousselham Ganbouri
%J Advances in Pure Mathematics
%P 93-97
%@ 2160-0384
%D 2014
%I Scientific Research Publishing
%R 10.4236/apm.2014.44015
%X <p class=\"MsoNormal\" style=\"text-align:justify;\">
	<span style=\"font-family:Verdana;\" lang=\"EN-US\">We study the Poisson-Lie structures on the group <em>SU</em>(2,R).
We calculate all Poisson-Lie structures on <em>SU</em>(2,R) through the correspondence
with Lie bialgebra structures on its Lie algebra <em>su</em>(2,R). We show that all
these structures are linearizable in the neighborhood of the unity of the group <em>SU</em>(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.</span> 
</p>
%K Poisson-Lie Structure
%K Lie Bialgebra
%K Hamiltonian
%K Poisson Automorphism
%K Linearization
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=44631