DUALITY OF CO-POISSON HOPF ALGEBRAS

Title & Authors
DUALITY OF CO-POISSON HOPF ALGEBRAS
Oh, Sei-Qwon; Park, Hyung-Min;

Abstract
Let A be a co-Poisson Hopf algebra with Poisson co-bracket $\small{\delta}$. Here it is shown that the Hopf dual $\small{A^{\circ}}$ is a Poisson Hopf algebra with Poisson bracket {f, g}(x) = < $\small{\delta(x)}$, $\small{f\;{\otimes}\;g}$ > for any f, g $\small{\in}$ $\small{A^{\circ}}$ and x $\small{\in}$ 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.
Keywords
co-Poisson Hopf algebra;Poisson Hopf algebra;
Language
English
Cited by
1.
Co-poisson structures on polynomial Hopf algebras, Science China Mathematics, 2017, 1869-1862
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