POISSON HOPF STRUCTURE INDUCED BY THE UNIVERSAL ENVELOPING ALGEBRA OF A GRADED LIE ALGEBRA

Abstract

Let G be an abelian group, α an antisymmetric bicharacter on G and g a (G, α)-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, α)-Poisson Hopf algebra.

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