Lie bialgebras arising from Poisson bialgebras

Sei-Qwon Oh; Eun-Hee Cho

doi:10.4134/JKMS.2010.47.4.705

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2010; 47(4): 705-718

Printed July 1, 2010

https://doi.org/10.4134/JKMS.2010.47.4.705

Lie bialgebras arising from Poisson bialgebras

Sei-Qwon Oh and Eun-Hee Cho

Chungnam National University, Chungnam National University

Abstract

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Abstract

It gives a method to obtain a natural Lie bialgebra from a Poisson bialgebra by an algebraic point of view. Let $\frak g$ be a coboundary Lie bialgebra associated to a Poission Lie group $G$. As an application, we obtain a Lie bialgebra from a sub-Poisson bialgebra of the restricted dual of the universal enveloping algebra $U(\frak g)$.

Keywords: Lie bialgebra, Poisson bialgebra

MSC numbers: Lie bialgebra, Poisson bialgebra