The K-inductive structure of the noncommutative Fourier transform - Walters, Samuel G. (MATHEMATICA SCANDINAVICA, 2019)
The noncommutative Fourier transform σ (U)=V^-1, σ (V)=U of the irrational rotation C*-algebra A_θ (generated by canonical unitaries U, V satisfying VU = e^2π iθ UV) is shown to have the following K-inductive structure (for a concrete class of irrational parameters, containing dense G_δ ’s). There are approximately central matrix projections e_1, e_2, f that are σ-invariant and which form a partition of unity in K_0 of the fixed-point orbifold A_θ ^σ , where f has the form f = g+σ (g) +σ ^2(g)+σ ^3(g), and where g is an approximately central matrix projection as well.