CHINESE ACAD SCI, GRAD SCH, BEIJING 100039, PEOPLES R CHINA
; CCAST, WORLD LAB, BEIJING 100080, PEOPLES R CHINA
; INST HIGH ENERGY PHYS, BEIJING 100039, PEOPLES R CHINA
In this paper, we introduce an NXN matrix is an element of(a ($) over bar b) in the quantum groups SUq(N) to transform the conjugate representation into the standard form so that we are able to compute the explicit forms of the important quantities in the bicovariant differential calculus on SUq(N), such as the q-deformed structure constant C-IJ(K) and the q-deformed transposition operator Lambda. From the q-gauge covariant condition we study the generalized q-deformed Killing form and construct the mth q-deformed Chern class P-m for the quantum groups SUq(N). In terms of the q-deformed homotopy operator we are able to compute the q-deformed Chern-Simons Q(2m-1) by the condition dQ(2m-1)=P-m. Furthermore, the q-deformed cocycle hierarchy, the q-deformed gauge covariant Lagrangian, and the q-deformed Yang-Mills equation are derived. (C) 1995 American Institute of Physics.