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

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DOI: 10.4236/apm.2014.44015    1,884 Downloads   2,954 Views  

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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Ganbouri, B. (2014) On the Structure of Infinitesimal Automorphisms of the Poisson-Lie Group SU(2,R). Advances in Pure Mathematics, 4, 93-97. doi: 10.4236/apm.2014.44015.

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