Advanced Search

We construct a class of quantum doubles $D\left(H_{D_n}\right)$ of pointed Hopf algebras of rank one $H_{𝒟}$. We describe the algebra structures of $D\left(H_{D_n}\right)$ by generators with relations. Moreover, we give the comultiplication ${\Delta }_D$, counit ${\epsilon }_D$ and the antipode $S_D$, respectively.