• Journal of the Korean Mathematical Society
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• v.47 no.4
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• pp.705-718
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• 2010

It gives a method to obtain a natural Lie bialgebra from a Poisson bialgebra by an algebraic point of view. Let 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(g).

• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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• pp.1685-1695
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• 2016

In this article we consider Lie super-bialgebra structures on the generalized loop super-Virasoro algebra ${\mathcal{G}}$. By proving that the first cohomology group $H^1({\mathcal{G}},{\mathcal{G}}{\otimes}{\mathcal{G}})$ is trivial, we obtain that all such Lie bialgebras are triangular coboundary.

• Communications of the Korean Mathematical Society
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• v.39 no.1
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• pp.11-30
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• 2024

3-Lie algebras are in close relationships with many fields. In this paper we are concerned with the study of 3-Hom-Lie super algebras, the concepts of 3-Hom-Lie coalgebras and how they make a 3-Hom-Lie superbialgebras, we study the structures of such categories of algebras and the relationships between each others. We study a super twisted 3-ary version of the Yang-Baxter equation, called the super 3-Lie classical Hom-Yang-Baxter equation (3-Lie CHYBE), which is a general form of 3-Lie classical Yang-Baxter equation and prove that the superbialgebras induced by the solutions of the super 3-Lie CHYBE induce the coboundary local cocycle 3-Hom-Lie superbialgebras.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.2
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• pp.307-310
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• 2015

Let H be a color Poisson bialgebra. Here we find a canonical nondegenerate bilinear form $\mathfrak{g}(H){\times}\mathfrak{m/m^2}$, where $\mathfrak{g}(H)$ and $\mathfrak{m/m^2}$ are certain color Lie algebras induced by H.