The crossed coproduct Hopf algebras
Bull. Korean Math. Soc. 2001 Vol. 38, No. 3, 527-541
Suk Bong Yoon
Dongeui University
Abstract : We find the necessary and sufficient conditions for the smash product algebra structure and the crossed coproduct coalgebra structure with the dual cocycle $\alpha$ to afford a Hopf algebra $B\bowtie^\alpha H$. If $B$ and $H$ are finite algebra and Hopf algebra, respectively, then the linear dual $(B\bowtie^\alpha H)^*$ is also a Hopf algebra. We show that the weak coaction admissible mapping system characterizes the new Hopf algebras $B\bowtie^\alpha H$.
Keywords : smash product, crossed coproduct, $\alpha$-Hopf algebra
MSC numbers : smash product, crossed coproduct, $\alpha$-Hopf algebra
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