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2013

Modules over the Noncommutative Torus and Elliptic Curves

D'Andrea, Francesco, Fiore, Gaetano, Franco, Davide

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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 $A_\theta$ of the noncommutative torus.
We show that such $A_\theta$-modules have a natural interpretation as Moyal deformations of vector bundles over an elliptic curve $E_\tau$, under the condition that the deformation parameter $\theta$ and the modular parameter $\tau$ satisfy a non-trivial relation.

Modules over the Noncommutative Torus and Elliptic Curves · Around

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