If G is any finite product of orthogonal, unitary and symplectic matrix groups, then Wilson loops generate a dense subalgebra of continuous observables on the configuration space of lattice gauge theory with structure group G. If G is orthogonal, unitary or symplectic, then Wilson loops associated to the natural representation of G are enough.This extends a result of A. Sengupta [7]. In particular, our approach includes the case of even orthogonal groups. IntroductionOn a compact Lie group, the Peter-Weyl theorem asserts that the characters of irreducible representations generate a dense subalgebra of continuous functions invariant by adjunction. In lattice gauge theory, configuration spaces are powers of a Lie group on which another power of the same group acts, according to the geometry of a given graph and in a way which extends the adjoint action of the group on itself. Peter-Weyl theorem can be adapted to this situation and the functions that play the role of the characters are called spin networks. Despite the fact that spin networks were introduced about forty years ago in a physical context 1 , their importance in lattice gauge theory has been recognized rather recently [1]. In the mean time, another set of functions, easier to define, has been used as the standard set of observables: Wilson loops. However, it is not clear at all a priori that this set is complete, that is, that Wilson loops generate a dense subalgebra of continuous invariant functions on the configuration space. A. Sengupta has proved in [7] that it is true when the group is a product of odd orthogonal, unitary (and symplectic) groups. In this paper, an approach similar to that of Sengupta but with a little more classical invariant theory combined with the use of spin networks allows us to add even orthogonal groups to the list and, hopefully, to clarify the argument. * IRMA -7, rue René Descartes -F-67084 Strasbourg Cedex 1 R. Penrose introduced them for the purposes of quantization of the geometry of space. See [8] for a historical account.