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Fourier Invariant Partially Approximating Subalgebras of the Irrational Rotation C*‐Algebra
Author(s) -
Walters S.
Publication year - 2004
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611503014503
Subject(s) - mathematics , subalgebra , irrational number , pure mathematics , invariant (physics) , algebra over a field , fourier transform , mathematics subject classification , rotation (mathematics) , mathematical analysis , geometry , mathematical physics
For a dense G δ ‐set of 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. 2000 Mathematics Subject Classification 46L80, 46L40, 46L35.