HOPF STRUCTURE FOR POISSON ENVELOPING ALGEBRAS

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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