S. Walters

For a dense $G_\delta$-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 Mathematical Subject Classification: 46L80, 46L40, 46L35.

Keywords: C*-algebras, irrational rotation algebras, automorphisms, inductive limits, K-groups, AF-algebras, theta functions.

E-mail:
walters@hilbert.unbc.ca