Generalized Heisenberg algebra from o(2, 4) Yang model

It is well known that the algebra o (2, 4) generates the conformal group, but it can also be used to define some variants of the Yang model of noncommutative geometry on a curved spacetime. Starting from these examples, we construct a new physical model based on o (2, 4), that can be interpreted as a generalization of the Heisenberg algebra n phase space, with flat positions and momenta, but nontrivial commutation relations between positions and momenta and with the Planck constant promoted to an operator.