Twisted product structure and representation theory of the quantum group Uq(2)

We present a construction of a compact quantum group, based on the method invented by Woronowicz, which uses a twisted determinant. In our case the result turns out to be the quantum group Uq(2). Our construction in a natural way shows that this group is a twisted product of its two quantum subgroups SUq(2) and U(1). This allows us to obtain description of irreducible unitary representations of Uq(2). We also give the construction of the multiplicative unitary (Kac-Takesaki) operator for this quantum group.