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\(C^*\)-algebras of dynamical systems on the non-commutative torus. (English) Zbl 0835.46059
Summary: Here, we prove that the \(C^*\)-algebras of dynamical systems on \({\mathcal A}_\rho\) associated to trace two affine automorphisms are classified by \(K\)-theoretical invariants. We also prove a partial classification result for the crossed products associated to general affine automorphisms induced by \(\text{SL}(2, \mathbb{Z})\) and compute their fixed point subalgebra.

MSC:
46L55 Noncommutative dynamical systems
46L80 \(K\)-theory and operator algebras (including cyclic theory)
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