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arXiv · 1307.6802

Modules over the Noncommutative Torus and Elliptic Curves

Francesco D'Andrea·Gaetano Fiore·Davide Franco
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Abstract

Using the Weil-Brezin-Zak transform of solid state physics, we describe line bundles over elliptic curves in terms of Weyl operators. We then discuss the connection with finitely-generated projective modules over the algebra $A_θ$ of the noncommutative torus. We show that such $A_θ$-modules have a natural interpretation as Moyal deformations of vector bundles over an elliptic curve $E_τ$, under the condition that the deformation parameter $θ$ and the modular parameter $τ$ satisfy a non-trivial relation.

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Francesco D'Andrea, Gaetano Fiore, Davide Franco. 2014-08-25. Modules over the Noncommutative Torus and Elliptic Curves. https://doi.org/10.1007/s11005-014-0718-x

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