COMPACT HOPF ASTERISK-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 Ko ornwinder. There exists an injective functor from the category of comp act Hopf -algebras to the category of compact Woronowicz algebras. A definition of the quantum enveloping algebra U-q(sl(n, C)) is given. F or quantum groups SUq(n) and SLq(n, C), the commutant of a canonical r epresentation of the quantum enveloping algebra for q coincides with t he commutant of the dual Woronowicz algebra for q(-1).