The Coalgebra Structure over Hom-Hopf Algebra
Received:October 30, 2014  Revised:March 09, 2015
Key Word: Hom-Hopf algebra   Hom-$\omega$-crossed coproduct   $\omega$-crossed coproduct
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 Author Name Affiliation Naifeng ZHENG Faculty of Science, Ningbo University, Zhejiang $315211$, P. R. China
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Let $(C,\alpha)$ and $(H,\beta)$ be Hom-bialgebras and $\omega:C\otimes H\rightarrow H\otimes C$ a linear map. We introduce the concept of a Hom-$\omega$-crossed coproduct $(C_{\omega}\bowtie_{\sigma} H,\gamma)$ and we give necessary and sufficient conditions for the new object to be a Hom-Hopf algebra.