  We apply the star product quantization to the Lie algebra. The quantization
in terms of the star product is well known and the commutation relation in this
case is called the $\theta$-deformation where the constant $\theta$ appears as
a parameter. In the application to the Lie algebra, we need to change the
parameter $\theta$ to $x$-dependent $\theta(x)$. There is no essential
difference between the quantization in the quantum mechanics and deriving
quantum numbers in the Lie algebra from the viewpoint of the star product. We
propose to unify them in higher dimensions, which may be analogous to the
Kaluza-Klein theory in the classical theory.
