The K-inductive structure of the noncommutative Fourier transform

• Samuel G. Walters ^[1]
  1. [1] University of Northern B.C. (Canadá)
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 124, Nº 2, 2019, págs. 305-319
• Idioma: inglés
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• Resumen

  • The noncommutative Fourier transform σ(U)=V−1, σ(V)=U of the irrational rotation C*-algebra Aθ (generated by canonical unitaries U, V satisfying VU=e2πiθUV) is shown to have the following K-inductive structure (for a concrete class of irrational parameters, containing dense Gδ's). There are approximately central matrix projections e1, e2, f that are σ-invariant and which form a partition of unity in K0 of the fixed-point orbifold Aσθ, where f has the form f=g+σ(g)+σ2(g)+σ3(g), and where g is an approximately central matrix projection as well.