Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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DUALITY OF CO-POISSON HOPF ALGEBRAS

  • Oh, Sei-Qwon (DEPARTMENT OF MATHEMATICS CHUNGNAM NATIONAL UNIVERSITY) ;
  • Park, Hyung-Min (DEPARTMENT OF MATHEMATICS CHUNGNAM NATIONAL UNIVERSITY)
  • Received : 2009.04.13
  • Published : 2011.01.31
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Abstract

Let A be a co-Poisson Hopf algebra with Poisson co-bracket $\delta$. Here it is shown that the Hopf dual $A^{\circ}$ is a Poisson Hopf algebra with Poisson bracket {f, g}(x) = < $\delta(x)$, $f\;{\otimes}\;g$ > for any f, g $\in$ $A^{\circ}$ and x $\in$ A if A is an almost normalizing extension over the ground field. Moreover we get, as a corollary, the fact that the Hopf dual of the universal enveloping algebra U(g) for a finite dimensional Lie bialgebra g is a Poisson Hopf algebra.

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References

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