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Letters in Mathematical Physics

, Volume 104, Issue 11, pp 1425–1443 | Cite as

Modules Over the Noncommutative Torus and Elliptic Curves

  • Francesco D’AndreaEmail author
  • Gaetano Fiore
  • Davide Franco
Article

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.

Mathematics Subject Classification

Primary 58B34 Secondary 46L87 53D55 

Keywords

noncommutative torus imprimitivity bimodules elliptic curves Moyal deformation 

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Francesco D’Andrea
    • 1
    • 2
    Email author
  • Gaetano Fiore
    • 1
    • 2
  • Davide Franco
    • 1
  1. 1.Dipartimento di Matematica e ApplicazioniUniversità di Napoli Federico IINaplesItaly
  2. 2.I.N.F.N., Sezione di Napoli, Complesso MSANaplesItaly

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