Hopf algebras constructed by the FRT-construction

Given any bialgebra A and a braiding product 〈|〉〈|〉 on A, a bialgebra U〈|〉U〈|〉 was constructed in [R. Larson, J. Towber, Two dual classes of bialgebras related to the concepts of “quantum group” and “quantum Lie algebra”, Comm. Algebra 19 (1991) 3295–3345], contained in the finite dual of AA. This construction generalizes a (not very well known) construction of Fadeev, Reshetikhin and Takhtajan [L.D. Faddeev, N.Yu. Reshetikhin, L.A. Takhtajan, Quantum Groups. Braid Group, Knot Theory and Statistical Mechanics, in: Adv. Ser. Math. Phys., vol. 9, World Sci. Publishing, Teaneck, NJ, 1989, pp. 97–110]. In the present paper it is proved that when U〈|〉U〈|〉 is finite-dimensional (even if AA is not), then it is a quasitriangular Hopf algebra.