Algebraic shape invariant models

Motivated by the shape invariance condition in supersymmetric quantum mechanics, we develop an algebraic framework for shape invariant Hamiltonians with a general change of parameters. This approach involves nonlinear generalizations of Lie algebras. Our work extends prsvious results showing the equivalence of shape invariant potentials involving a translational change of parameters with a standard SO(2, 1) potential algebra for Natanzon type potentials.