### Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 10 (2014), 029, 14 pages      arXiv:1103.6054      https://doi.org/10.3842/SIGMA.2014.029
Contribution to the Special Issue on Noncommutative Geometry and Quantum Groups in honor of Marc A. Rieffel

### On Projections in the Noncommutative 2-Torus Algebra

Michał Eckstein
Faculty of Mathematics and Computer Science, Jagellonian University, ul. Łojasiewicza 6, 30-348 Kraków, Poland

Received December 09, 2013, in final form March 16, 2014; Published online March 23, 2014

Abstract
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 $A_{\theta}$.

Key words: noncommutative torus; projections; noncommutative solitons.

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