# The K-inductive Structure of the Noncommutative Fourier Transform

## TL;DR

This paper demonstrates that the noncommutative Fourier transform of certain irrational rotation C*-algebras possesses a K-inductive structure, extending the understanding of automorphisms in noncommutative geometry.

## Contribution

It introduces a K-inductive structure for the noncommutative Fourier transform in irrational rotation C*-algebras, generalizing the tracially AF concept with additional structural requirements.

## Key findings

- K-inductive structure established for a large class of irrational parameters
- Structure analogous to Huaxin Lin's tracially AF but with extra projection conditions
- Results applicable to dense G_delta sets of parameters

## 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.