Decomposable projections related to the Fourier and flip automorphisms

Authors

  • S. Walters

DOI:

https://doi.org/10.7146/math.scand.a-15150

Abstract

In this paper we classify Fourier invariant projections $g$ in the irrational rotation $C^*$-algebra that can be decomposed in the form 26741 g = f + \sigma(f) + \sigma^2(f) + \sigma^3(f) 26741 for some Fourier orthogonal projection $f$, where $\sigma$ is the Fourier transform automorphism. The analogous result is shown for the flip automorphism as well as the existence of flip-orthogonal projections. Both classifications are achieved by means of topological invariants (given by unbounded traces) and the canonical trace. We also show (in both the flip and Fourier cases) that invariant projections $h$ are subprojections of orthogonal decompositions $g$ for some projection $f$ such that $\tau(f) = \tau(h)$ (where $\tau$ is the canonical trace).

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Published

2010-12-01

How to Cite

Walters, S. (2010). Decomposable projections related to the Fourier and flip automorphisms. MATHEMATICA SCANDINAVICA, 107(2), 174–197. https://doi.org/10.7146/math.scand.a-15150

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Section

Articles