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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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