Fourier Invariant Partially approximating subalgebras of the irrational rotation C*-algebra

Details Fourier Invariant Partially approximating subalgebras of the irrational rotation C*-algebra Fourier Invariant Partially approximating subalgebras of the irrational rotation C*-algebra

2001-06-07

arxiv.org/abs/math/0106053v1

Mathematics

Operator Algebras

20 pages

Scientific paper

For all transcendental parameters, the irrational rotation algebra is shown to contain infinitely many C*-subalgebras satisfying the following properties. Each subalgebra is isomorphic to a direct sum of two matrix algebras of the same (perfect square) dimension; the Fourier transform maps each summand onto the other; the corresponding unit projection is approximately central; the compressions of the canonical generators of the irrational rotation algebra are approximately contained in the subalgebra.

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