Reduced Yang model and noncommutative geometry of curved spacetime

The Yang model describes a noncommutative geometry in a curved spacetime by means of an orthogonal algebra [Formula: see text], whose 15 generators are identified with phase space variables and Lorentz generators, together with an additional scalar generator. In this paper, we show that it is possible to define a nonlinear algebra with the same structure, but with only 14 generators, that better fits in phase space. The 15 generators of the Yang algebra can then be written as a function of the squares of the others. As a simple application, we also consider the problem of the quantum harmonic oscillator in this theory, calculating the energy spectrum in the one- and three-dimensional nonrelativistic versions of the model.