LIE BIALGEBRA ARISING FROM POISSON BIALGEBRA U(sp4)

  • Oh, Sei-Qwon (Department of Mathematics Chungnam National University) ;
  • Hyun, Sun-Hwa (Department of Mathematics Chungnam National University)
  • Received : 2007.11.24
  • Published : 2008.03.31

Abstract

Let $U(sp_4)$ be the universal enveloping algebra of the symplectic Lie algebra $sp_4$. Then the restricted dual $U(sp_4)^{\circ}$ becomes a Poisson Hopf algebra with the Sklyanin Poisson bracket determined by the standard classical r-matrix. Here we illustrate a method to obtain the Lie bialgebra from a Poisson bialgebra $U(sp_4)^{\circ}$.

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