  It is shown that the generators of two discrete Heisenberg-Weyl groups with
irrational rotation numbers $\theta$ and $-1/ \theta$ generate the whole
algebra $\cal B$ of bounded operators on $L_2(\bf R)$. The natural action of
the modular group in $\cal B$ is implied. Applications to dynamical algebras
appearing in lattice regularization and some duality principles are discussed.
