• 대한수학회보
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• 제38권3호
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• pp.527-541
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• 2001

We find the necessary and sufficient conditions for the smash product algebra structure and the crossed coproduct coalgebra structure with th dual cocycle $\alpha$ to afford a Hopf algebra (A equation,※See Full-text). If B and H are finite algebra and Hopf algebra, respectively, then the linear dual (※See Full-text) is also a Hopf algebra. We show that the weak coaction admissible mapping system characterizes the new Hopf algebras (※See Full-text).

• 충청수학회지
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• 제23권1호
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• pp.177-184
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• 2010

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