Compact Hopf *-algebras, quantum enveloping algebras and dual Woronowicz algebras for quantum Lorentz groups

A compact Hopf *-algebra is a compact quantum group in the sense of Koornwinder. There exists an injective functor from the category of compact Hopf *-algebras to the category of compact Woronowicz algebras. A definition of the quantum enveloping algebra U-q(sl(n, C)) is given. For quantum groups SUq(n) and SLq(n, C), the commutant of a canonical representation of the quantum enveloping algebra for q coincides with the commutant of the dual Woronowicz algebra for q(-1).