  In quantum physics, the operators associated with the position and the
momentum of a particle are unbounded operators and $C^*$-algebraic quantisation
does therefore not deal with such operators. In the present article, I propose
a quantisation of the Lie-Poisson structure of the dual of a Lie algebroid
which deals with a big enough class of functions to include the above mentioned
example. As an application, I show with an example how the quantisation of the
dual of the Lie algebroid associated to a Poisson manifold can lead to a
quantisation of the Poisson manifold itself. The example I consider is the
torus with constant Poisson structure, in which case I recover its usual
$C^*$-algebraic quantisation.
