Let V be a multiplicative unitary operator on a separable Hilbert spaceH, then there are two subalgebras ofB( H) denoted byA( V) and ?( V), respectively, which correspond to V. If V satisfiesV 2 =I, then we will obtai...Let V be a multiplicative unitary operator on a separable Hilbert spaceH, then there are two subalgebras ofB( H) denoted byA( V) and ?( V), respectively, which correspond to V. If V satisfiesV 2 =I, then we will obtain the necessary and sufficient condition of Baaj and Skandalis’ main theorem, i.e.V has a Kac-system if and only if the linear closed space of the product of the above two algebras is the compact operator space; with this condition the above algebras are also quantum groups.展开更多
In this paper,we generalize the Takesaki-Takai duality theorem in Hilbert C~*-modules; that is to say,if (H,V,U) is a Kac-system,where H is a Hilbert space,V is a multiplicative unitary operator on H(?)H and U is a un...In this paper,we generalize the Takesaki-Takai duality theorem in Hilbert C~*-modules; that is to say,if (H,V,U) is a Kac-system,where H is a Hilbert space,V is a multiplicative unitary operator on H(?)H and U is a unitary operator on H,and if E is an (?)-compatible Hilbert (?)-module, then E×(?)×(?)K(H),where K(H) is the set of all compact operators on H,and (?) and (?) are Hopf C~*-algebras corresponding to the Kac-system (H,V,U).展开更多
In this paper,it is shown that the regular representation and regular covariant representation of the crossed products A×αG correspond to the twisted multiplicative unitary operators,where A is a Woronowicz C~*-...In this paper,it is shown that the regular representation and regular covariant representation of the crossed products A×αG 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.展开更多
文摘Let V be a multiplicative unitary operator on a separable Hilbert spaceH, then there are two subalgebras ofB( H) denoted byA( V) and ?( V), respectively, which correspond to V. If V satisfiesV 2 =I, then we will obtain the necessary and sufficient condition of Baaj and Skandalis’ main theorem, i.e.V has a Kac-system if and only if the linear closed space of the product of the above two algebras is the compact operator space; with this condition the above algebras are also quantum groups.
基金Supported by NSF 10301004,NSF 10171098Yantai University PHD Foundation SX03B14
文摘In this paper,we generalize the Takesaki-Takai duality theorem in Hilbert C~*-modules; that is to say,if (H,V,U) is a Kac-system,where H is a Hilbert space,V is a multiplicative unitary operator on H(?)H and U is a unitary operator on H,and if E is an (?)-compatible Hilbert (?)-module, then E×(?)×(?)K(H),where K(H) is the set of all compact operators on H,and (?) and (?) are Hopf C~*-algebras corresponding to the Kac-system (H,V,U).
基金supported by the National Natural Science Foundation of China(Grant Nos.10301004&10171098)Yantai University PhD Foundation(Grant No.SX03B14).
文摘In this paper,it is shown that the regular representation and regular covariant representation of the crossed products A×αG 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.
