Representations and automorphisms of the irrational rotation algebra (Q1065332)

It is known that the representation theory of an irrational rotation algebra \(A_{\alpha}\) is rather complicated. Let U, V be generators of \(A_{\alpha}\) satisfying the relation \(UV=\exp (2\pi i\alpha)VU\). The author has succeeded to describe all separable representations of \(A_{\alpha}\) which have uniform multiplicity m(m') when restricted to the abelian *-subalgebra generated by U(V). The invariants needed for their classification are m, a measure \(\nu\) on the unit circle which is quasi-invariant under \(\alpha\)-rotations, and a certain unitary 1-cocycle on integers. Other topics considered are: existence of irreducible representations of \(A_{\alpha}\) with arbitrary relatively prime m, m'; factor representations and ergodicity of \(\nu\) ; action of SL(2,\({\mathbb{Z}})\) by automorphisms of \(A_{\alpha}\); pure states and their equivalence.