Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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POISSON HOPF STRUCTURE INDUCED BY THE UNIVERSAL ENVELOPING ALGEBRA OF A GRADED LIE ALGEBRA

  • Oh, Sei-Qwon (Department of Mathematics Chungnam National University) ;
  • Park, Miran (Department of Mathematics Chungnam National University)
  • Received : 2010.02.08
  • Accepted : 2010.03.08
  • Published : 2010.03.30
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Abstract

Let G be an abelian group, $\alpha$ an antisymmetric bicharacter on G and g a (G, $\alpha$)-Lie algebra. Here we give a complete proof for that the associated graded algebra determined by a natural filtration in the universal enveloping algebra U(g) is a (G, $\alpha$)-Poisson Hopf algebra.

Keywords

Acknowledgement

Supported by : Korea Research Foundation

References

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  2. J. Dixmier, Enveloping algebras, The 1996 printing of the 1977 English translation Graduate Studies in Mathematics, vol. 11, American Mathematical Society, Providence, 1996.
  3. Sei-Qwon Oh, Graded Lie bialgebras, submitted (2009).