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A family of states built from the uncertainty principle on the fuzzy spherehas been shown to reproduce the stereographic projection in the large $j$limit. These generalized squeezed states are used to construct an associativestar product which involves a finite number of derivatives on its primaryfunctional space. It is written in terms of a variable on the complex plane. Weshow that it actually coincides with the one found by H.Gross and P.Presnajderin the simplest cases, endowing the later with a supplementary physicalinterpretation. We also show how the spherical harmonics emerge in thissetting.Comment: 14 pages, version to appear in PR

Fuzzy sphere: Star product induced from generalized squeezed states