The fuzzy S4 by quantum deformation Original Research Article

The fuzzy algebra of S4 is discussed by quantum deformation. To this end we embed the classical S4 in the Kähler coset space SO(5)/U(2). The harmonic functions of S4 are constructed in terms of the complex coordinates of SO(5)/U(2). Being endowed with the symplectic structure they can be deformed by the Fedosov formalism. We show that they generate the fuzzy algebra Â∞(S4) under the ★ product defined therein, by using the Darboux coordinate system. The fuzzy spheres of higher even dimensions can be discussed similarly. We give basic arguments for the generalization as well.