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 o(1,5), 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.