The compact quantum group Uq(2) I

Corresponding to Hayashi’s R-matrix, we first follow Woronowicz’s method to construct an other concrete compact quantum group Uq(2), ; then we discuss its *-irreducible representations, and we show that these representations correspond to those of irrational algebras Bθ, and in the final, we also give the formula of Haar measure of Uq(2).