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We find a dual version of a previous double-bosonisation theorem whereby eachfinite-dimensional braided-Hopf algebra $B$ in the category of comodules of acoquasitriangular Hopf algebra $A$ has an associated coquasitriangular Hopfalgebra $B^{\underline{\rm op}}\rtimes A \ltimes B^*$. As an application wefind new generators for $c_q[SL_{2}]$ reduced at $q$ a primitive odd root ofunity with the remarkable property that their monomials are essentially a dualbasis to the standard PBW basis of the reduced Drinfeld-Jimbo quantumenveloping algebra $u_q(sl_{2})$. Our methods apply in principle for general$c_{q}[G]$ as we demonstrate for $c_q[SL_3]$ at certain odd roots of unity.

Co-double bosonisation and dual bases of c_q[SL_2] and c_q[SL_3]