ACAD SINICA,GRAD SCH,BEIJING 100039,PEOPLES R CHINA
; CCAST WORLD LAB,BEIJING 100081,PEOPLES R CHINA
; INST HIGH ENERGY PHYS,BEIJING 100039,PEOPLES R CHINA
Based on the q-deformed BRST algebra of Bernard and Watamura, we study the q-deformed Killing form and the second q-deformed Chem class for the quantum group SUq(2) from the q-gauge covariant condition. We find that although the components of the identity and the adjoint representations are mixed in the covariant commutative relations of the q-deformed BRST algebra, the q-deformed Chem class can be defined uniquely up to a common factor such that it contains only adjoint components. We compute the q-deformed Chern-Simons by introducing a q-deformed homotopy operator, that is the quantum analogue of the homotopy operator presented by Chem and Zumino. Finally, we calculate the q-deformed cocycle hierarchy.