Differential Hopf algebra structure of the quantum standard complex

We are investigating the quantum standard complex (K(q,g),d) of the quantum enveloping algebra U-q(g) for Lie algebras g associated with the root systems, A(n), B-n, C-n, and D-n. It is a quantum version of the standard Koszul complex associated to a Lie algebra as applied for instance in the BRS quantization procedure in connection with spin representations. Using techniques from the theory of braided monoidal categories we obtain a differential Hopf algebra structure on the complex (K(q,g),d). (C) 1997 American Institute of Physics.