Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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HOPF STRUCTURE FOR POISSON ENVELOPING ALGEBRAS

  • Min, Kangju (Department of Mathematics Chungnam National University) ;
  • Oh, Sei-Qwon (Department of Mathematics Chungnam National University)
  • Received : 2000.12.01
  • Published : 2001.01.10
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Abstract

For a Poisson Hopf algebra A, we find a natural Hopf structure in the Poisson enveloping algebra U(A) of A. As an application, we show that the Poisson enveloping algebra U(S(L)), where S(L) is the symmetric algebra of a Lie algebra L, has a Hopf structure such that a sub-Hopf algebra of U(S(L)) is Hopf-isomorphic to the universal enveloping algebra of L.

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