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.