Sur la structure des algèbres de Kac,I

We elaborate on the relative situation of a Kac algebra and its dual, then, introducing three invariants we obtain a generalization of Heisenberg's commutation relations. Using the operator-valued weights introduced by U. Haagerup, we give a simpler definition for Kac algebras. As an application, we generalize the unicity of the left Haar measure on a locally compact group.