($f,\omega$)-Compatible Pair $(B,H)$ for $\omega$-Smash Coproduct Hopf Algebras
Received:December 25, 2007  Revised:July 06, 2008
Key Word: $\omega$-smash coproduct Hopf algebras   $(f,\omega)$-compatible pair   Yetter-Drinfeld category.
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.60873267).
 Author Name Affiliation Nai Feng ZHENG Faculty of Science, Ningbo University, Zhejiang 315211, P. R. China
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In this paper we introduce the notion of $(f,\omega)$-compatible pair $(B,H)$, by which we construct a Hopf algebra in the category $^H_H$YD of Yetter-Drinfeld $H$-modules by twisting the comultiplication of $B$. We also study the property of $\omega$-smash coproduct Hopf algebras $B_{\omega}\bowtie H$.