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Keywords:
pointed Hopf algebra; quantum double; rank one
pointed Hopf algebra; quantum double; rank one
Summary:
We construct a class of quantum doubles $D(H_{D_n})$ of pointed Hopf algebras of rank one $H_{\mathcal {D}}$. We describe the algebra structures of $D(H_{D_n})$ by generators with relations. Moreover, we give the comultiplication $\Delta _{D}$, counit $\varepsilon _D$ and the antipode $S_{D}$, respectively.
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