On Projections in the Noncommutative 2-Torus Algebra

We investigate a set of functional equations defining a projection in the noncommutative 2-torus algebra $A_{\theta}$. The exact solutions of these provide various generalisations of the Powers–Rieffel projection. By identifying the corresponding $K_0(A_{\theta})$ classes we get an insight into the structure of projections in $A_{\theta}$.