Noncommutative $R^d$ via closed star product

Understand

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, $Tr( f\star g)= Tr( f\cdot g)$.