  We show that the non-Abelian nature of geometric fluxes---the corner-stone in
the definition of quantum geometry in the framework of loop quantum gravity
(LQG)---follows directly form the continuum canonical commutations relations of
gravity in connection variables and the validity of the Gauss law. The present
treatment simplifies previous formulations and thus identifies more clearly the
root of the discreteness of geometric operators in LQG. Our statement
generalizes to arbitrary gauge theories and relies only on the validity of the
Gauss law.
