Coherent State Induced Star-Product on $R^3_{lambda}$ and the Fuzzy Sphere

Using the Hopf fibration and starting from a four dimensional noncommutative Moyal plane, $R^2_{theta}times R^2_{theta}$, we obtain a star-product for the noncommutative (fuzzy) $R^3_{lambda}$ defined by $[x^i,x^j]=ilambdaepsilon_{ijk}x^k$. Furthermore, we show that there is a projection function which allows us to reduce the functions on $R^3_{lambda}$ to that of the fuzzy sphere, and hence we introduce a new star-product on the fuzzy sphere. We will then briefly discuss how using our method one can extract information about the field theory on fuzzy sphere and $rrlam$ from the corresponding field theories on $R_{theta}times R_{theta}$ space.