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The Schr\"{o}dinger equation in three dimensional space with constantpositive curvature is studied for the Mie potential. Using analytic polynomialsolutions, we have obtained whole spectrum of the corresponding system. Withthe aid of factorization method, ladder operators are obtained within thevariable and function transformations. Using ladder operators, we have giventhe generators of $so(2,1)$ algebra and the Casimir operator which are relatedto the Mie Oscillator on the positive curvature.

$su(1,1)\simeq so(2,1)$ Lie Algebraic Extensions of the Mie-type Interactions with Positive Constant Curvature