Bicovariant calculus in quantum theory and a generalization of the Gauss law

We construct a deformation of the quantum algebra Fun(T*G) associated with Lie group G to the case where G is replaced by a quantum group G(q) which h as a bicovariant calculus. The deformation easily allows for the inclusion of the current algebra of left and right invariant one forms. We use it to examine a possible generalization of the Gauss law commutation relations fo r gauge theories based on G(q). (C) 2000 Elsevier Science B.V. All rights r eserved.