Correction to: “Braided quantum groups and their bosonizations in the C*-algebraic framework”

Suppose |$\mathcal {C}$| is the category of unitary representations of the quantum codouble of a |$\textrm {C}^{\ast }$|-quantum group |$\mathbb {G}$| on separable Hilbert spaces. Then |$\mathcal {C}$| is a braided monoidal category and the braiding operators are unitaries. Suppose |${\includegraphics{\bwartpath rnac324fx1}}$| is a braiding unitary in |$\mathcal {C}$|⁠. Then the dual of |${\includegraphics{\bwartpath rnac324fx2}}$| is defined by |${\includegraphics{\bwartpath rnac324fx3}}$|⁠. In [1] the braiding operators appear in the place of its dual braiding operators. In this note, we correct those typos and their consequences. In the right hand side of [1, Equation (1.3)], second braiding operator |${\includegraphics{\bwartpath rnac324fx4}}$| should be replaced by the dual braiding operator |${\includegraphics{\bwartpath rnac324fx5}}$| and the correct equation is the following: ... In the statement of [1, Theorem 2.22] the correct definition of |$j_{2}$| is |$j_{2}(c_{2})={\includegraphics{\bwartpath rnac324fx10}}$|⁠, where |${\includegraphics{\bwartpath rnac324fx11}}$|⁠. In the second paragraph of [1, Section 5.1], the correct definition of the dual of |$\mathbb{F} $| is |${\includegraphics{\bwartpath rnac324fx12}}$|⁠. In the paragraph after [1, Equation (5.11)], the definition of |$\iota _{2}$| is |$\iota _{2}({\hat{b}})\break{\includegraphics{\bwartpath rnac324fx13}}$|⁠. In the first paragraph of [1, Section 6.3.1], the correct equation in the third line is |${\includegraphics{\bwartpath rnac324fx14}} $| and the correct braiding operator appearing in the sixth line is |${\includegraphics{\bwartpath rnac324fx15}}$|⁠.