The compact quantum group Uq (2) I

Abstract Corresponding to Hayashi’s R -matrix, we first follow Woronowicz’s method to construct an other concrete compact quantum group U q (2), q ∈ C ⧹ { 0 } ; then we discuss its *-irreducible representations, and we show that these representations correspond to those of irrational algebras B θ , and in the final, we also give the formula of Haar measure of U q (2).