The dual of a certain left quantum group. (Q2797027)

Using only some of the relations of \(SL_q(2)\), \textit{S. Rodríguez-Romo} and \textit{E. J. Taft} [J. Algebra 286, No. 1, 154-160 (2005; Zbl 1073.16033)] constructed a bialgebra \(\widetilde{SL_q(2)}\) which has a linear endomorphism satisfying the left antipode condition, but not the right antipode condition. Thus \(\widetilde{SL_q(2)}\) is a left Hopf algebra, but not a Hopf algebra. -- In the paper under review, the authors show that the finite duals \(SL_q(2)^0\) and \(\widetilde{SL_q(2)}^0\) are isomorphic as left Hopf algebras. In particular, \(\widetilde{SL_q(2)}^0\) is a Hopf algebra.