Shahn Majid and Eliezer Batista find the derivative of a wave plane in their paper:
Non Commutative Geometry of Angular Momentum Space $U \mathfrak{su}(2)$.
They obtained the non commutating relations between one form:
$x_a dx_b=(dx_b)x_a+\frac{i \lambda}{2} \epsilon_{abc} dx_c+\frac{\lambda}{4} \delta_{ab} \theta$
$x_a \theta=\theta x_a +\lambda dx_a$
They also find that:
$df(x)=(dx_a)\partial^a f(x)+\frac{\theta}{c} \partial^0 f(x)$
How can they deduce that:
$de^{ik.x}=\left\{\frac{\theta}{\lambda}\left(\cos \left(\frac{\lambda \vert k \vert}{2}\right)-1\right)+\frac{2i \sin\left(\frac{\lambda \vert k \vert}{2}\right)}{\lambda \vert k \vert} k. dx \right\} e^{ik.x}\quad?$