The K-inductive Structure of the Noncommutative Fourier Transform

Abstract

The noncommutative Fourier transform of the irrational rotation C*-algebra is shown to have a K-inductive structure (at least for a large concrete class of irrational parameters, containing dense $G_\delta$'s). This is a structure for automorphisms that is analogous to Huaxin Lin's notion of tracially AF for C*-algebras, except that it requires more structure from the complementary projection.