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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.
The purpose of this article is to answer this question. At the same time, it seems appropriate to ask whether such inductive limit structure does not obtain more generally. (There are in fact already other results of a similar nature).

MSC:
46L55 Noncommutative dynamical systems
46M40 Inductive and projective limits in functional analysis
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