The regular representation and regular covariant representation of crossed products of Woronowicz C^(*)-algebras

In this paper,it is shown that the regular representation and regular covariant representation of the crossed products A×α G correspond to the twisted multiplicative unitary operators,where A is a Woronowicz C~*-algebra acted upon by a discrete group G.Meanwhile,it is also shown that the regular covariant C~*-algebra is the Woronowicz C~*-algebra which corresponds to a multiplicative unitary.Finally,an explicit description of the multiplicative unitary operator for C(SU_q(2) )×α (?) is given in terms of those of the Woronowicz C~*-algebra C(SU_q(2) ) and the discrete group G.

In this paper, it is shown that the regular representation and regular covariant representation of the crossed products A×α G correspond to the twisted multiplicative unitary operators, where A is a Woronowicz C*-algebra acted upon by a discrete group G. Meanwhile, it is also shown that the regular covariant C*-algebra is the Woronowicz C*-algebra which corresponds to a multiplicative unitary. Finally, an explicit description of the multiplicative unitary operator for C(SUq(2))×α Z is given in terms of those of the Woronowicz C*-algebra C(SUq(2)) and the discrete group G.