  We consider linear star products on $R^d$ of Lie algebra type. First we
derive the closed formula for the polydifferential representation of the
corresponding Lie algebra generators. Using this representation we define the
Weyl star product on the dual of the Lie algebra. Then we construct a gauge
operator relating the Weyl star product with the one which is closed with
respect to some trace functional, $Tr( f\star g)= Tr( f\cdot g)$. We introduce
the derivative operator on the algebra of the closed star product and show that
the corresponding Leibnitz rule holds true up to a total derivative. As a
particular example we study the space $R^3_\theta$ with $\mathfrak{su}(2)$ type
noncommutativity and show that in this case the closed star product is the one
obtained from the Duflo quantization map. As a result a Laplacian can be
defined such that its commutative limit reproduces the ordinary commutative
one. The deformed Leibnitz rule is applied to scalar field theory to derive
conservation laws and the corresponding noncommutative currents.
