Acad Sinica, Inst High Energy Phys, Beijing 100039, Peoples R China
; CCAST, World Lab, Beijing 100080, Peoples R China
; Acad Sinica, Inst Theoret Phys, Beijing 100080, Peoples R China
Relationships between quantum group and quantum universal enveloping algebra are investigated. We present what is called the quantum Ashkin-Teller model with general nearest-neighbour four interaction terms. In the case of vanishing four interaction, it reduces to two decoupled XXZ chains with surface terms, which has been studied thoroughly in the framework of quantum universal enveloping algebra symmetry. It is shown that the symmetry structure of the quantum version of Ashkin-Teller model is the quantum group SLq(2). This quantum group structure guarantees the integrability of the quantum model.