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The structure of the irrational rotation $$C^*$$-algebra. (English) Zbl 0847.46034
For some time, it has been a question whether the well-known irrational rotation $$C^*$$-algebra, $$A_\theta$$, is an inductive limit of $$C^*$$-algebras of type I. This $$C^*$$-algebra, and its higher-dimensional analogues, are of fundamental importance.