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On projections in the noncommutative 2-torus algebra. (English) Zbl 1298.46062

Summary: We investigate a set of functional equations defining a projection in the noncommutative 2-torus algebra \(A_{\theta}\). The exact solutions of these provide various generalisations of the Powers-Rieffel projection. By identifying the corresponding \(K_0(A_{\theta})\) classes we get an insight into the structure of projections in \(A_{\theta}\).

MSC:

46L87 Noncommutative differential geometry
46L80 \(K\)-theory and operator algebras (including cyclic theory)
19A13 Stability for projective modules
19K14 \(K_0\) as an ordered group, traces
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